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Let X be a random number between 0 and 1 produced by the idealized uniform random number generator. Use the density curve for X, shown below, to find the probabilities: (a) P(0.3≤X≤0.7) = (b) P(X=0.89) =

(a) .4 (b) 0 Explanation: (a) 7-3 (b) = is always 0

The amounts of 6 restaurant bills and the corresponding amounts of the tips are given in the below. Assume that bill amount is the explanatory variable and tip amount the response variable. If the amount of the bill is $90, the best prediction for the amount of the tip is _______

$13.60 Explanation: Plug it into the equation

If x is a binomial random variable, compute the mean, the standard deviation, and the variance for each of the following cases: (a) n=3, p=0.6 μ= σ2= σ= (b) n=6, p=0.7 μ= σ2= σ= (c) n=4, p=0.3 μ= σ2= σ= (d) n=5, p=0.8 μ= σ2= σ=

(a) μ= 1.8 σ2= .72 σ=.848 (b) μ= 4.2 σ2= 1.26 σ= 1.122 (c) μ= 1.2 σ2= .84 σ= .916 (d) μ= 4 σ2= .8 σ= .894 Explanation: -Mean = np -Variance = n x p x (1-p) -Standard deviation = sqrt (n x p x (1-p))

About 2.5 percent of all men are shorter than what height? A. 74 inches B. 64 inches. C. 61.5 inches D. 66.5 inches E. None of the above.

B. 64 inches. Explanation: 2.5% is 2 standard deviations away from the mean, making it 64

(b) How many surgeons are not hospital-based? A. 24,128 B. 77,700 C. 25,901 D. 73,970 E. None of the above.

B. 77,700 Explanation: Count

For a biology project, you measure the weight in grams and the tail length in millimeters of a group of mice. The correlation is r = 0.1. If you had measured tail length in centimeters instead of millimeters, what would be the correlation? (There are 10 millimeters in a centimeter.) A. 0.1/10 = 0.01 B. (0.1)(10) = 1 C. 0.1 D. None of the above.

C. 0.1 Explanation: Correlation does not change when units change

About what percent of men are shorter than 66.5 inches? A. 32% B. 2.5% C. 16% D. 5% E. None of the above.

C. 16% Explanation: After making the empirical rule and figuring out the standard deviations between them all, you find that 66.5 inches is one standard deviation down from the mean. From there, we can find that everything below the 66.5 line would equal 16%

What electrical changes occur in muscles as they get tired? Student subjects hold their arms above their shoulders until they have to drop them. Meanwhile, the electrical activity in their arm muscles is measured. This is A. a randomized comparative experiment. B. an observational study. C. an experiment with no control group. D. None of the above.

C. an experiment with no control group. Explanation: Things are manipulated so experiment. There is no control group where they do not lift their shoulders

Yes Explanation: The closer to 1, the higher the significance of the correlation

A group of psychologists carried out 77 separate significance tests and found that two were significant at the 5% level. Suppose that the tests are independent of each other. (In fact, they were not independent because all involved the same subjects.) If all of the null hypotheses are true, then each test has probability 0.05 of being significant at the 5% level. Compute the probability that two or more of the tests are significant.

0.902672574 Explanation: see pic

1. A two-tail test is a test in which a null hypothesis can be rejected by an extreme result occurring in only one direction. 2. The PP-value is usually 0.05. 3. The probability of a Type I error is represented by β, and is the probability of failing to reject a false null hypothesis. 4. The P-value of a test is the probability of observing a test statistic at least as extreme as the one computed given that the null hypothesis is true.

1. False 2. False 3. Fasle 4. True

An airline has determined that the relationship between the number of passengers on a flight and the total weight of luggage stored in the baggage compartment can be estimated by the least squares regression equation y=216+27x. Predict the weight of luggage for a flight with 47 passengers.

1485 pounds Explanation: Calculator

A study was conducted to determine whether the final grade of a student in an introductory psychology course is linearly related to his or her performance on the verbal ability test administered before college entrance. The verbal scores and final grades for 1010 students are shown in the table below. Calculate the residual for the fifth student

16.115 Explanation: Residual is observed value - predicted value

The Trial Urban District Assessment (TUDA) is a government-sponsored study of student achievement in large urban school districts. TUDA gives a reading test scored from 0 to 500. A score of 243 is a "basic" reading level, and a score of 281 is proficient. Scores for a random sample of 3000 eight-graders in Atlanta had x¯=250 with standard error 11. Give a 80% confidence interval for the mean score of all Atlanta eight graders.

248.718 < μ < 251.281 Explanation: T-Interval in Excel and pic

Healthy men aged 21 to 35 were randomly assigned to one of two groups: half received 0.820.82 grams of alcohol per kilogram of body weight; half received a placebo. Participants were given thirty minutes to read up to 34 pages of Tolstoy's War and Peace. Every two to four minutes participants were prompted to indicate whether they were "zoning out". The proportion of times participants indicated they were zoning out was recorded for each subject, with the results summarized in the following table. Is there evidence to show that the men drinking alcohol "zoned out" more often? Treatment Sample Size: 25 Treatment Mean: 0.25 Treatment Standard Error of the Mean: 0.05 Placebo Sample Size: 25 Placebo Mean: 0.12 Placebo Standard Error of the Mean: 0.03 (a) What is the P-value for this test? (b) The conclusion is A. There is not sufficient evidence to conclude that men drinking alcohol zoned out more often. B. There is strong evidence to conclude that men drinking alcohol zoned out more often.

(a) .0158 (b) B. There is strong evidence to conclude that men drinking alcohol zoned out more often. Explanation: 2-SampTTest in excel, see pic

In a study of exercise, a large group of male runners walk on a treadmill for 6 minutes. After this exercise, their heart rates vary with mean 8.6 per five seconds and standard deviation 1.1 per five seconds. Let x¯ be the mean number of heartbeats per five seconds after measuring heart rate for 12 five-second intervals (a minute). (a) What is the approximate probability that x¯ is less than 8? (b) What is the probability that the heart rate of a runner is less than 100 beats per minute? Hint : Restate this event in terms of x¯.

(a) .02941 (b) .20051 Explanation: see pic

A two-sample t test was performed to determine if the lifetimes (in hours) of batteries differ between a name brand and a generic. The output from SPSS, a popular statistical package, is shown below. (a) What is the P-value for this test? (b) Using a significance level of 5%, the conclusion is A. There is evidence to conclude that the name brand and generic batteries have different average lifetimes. B. There is not sufficient evidence to conclude that the name brand and generic batteries have different average lifetimes.

(a) .031 (b) A. There is evidence to conclude that the name brand and generic batteries have different average lifetimes. Explanation Answer in problem, unequal variances

Do educational programs for preschool children that follow the Montessori method perform better than other programs? A study compared 55-year-old children in Milwaukee, Wisconsin, who had been enrolled in preschool programs from the age of 33. Test scores for random 55-year-old children are recorded in the table below. At a 5% level, is there evidence that children educated in Montessori programs perform differently than children in other programs? Montessori Sample Size: 30 Montessori Mean: 19 Montessori Standard Deviation: 3.11 Control Sample Size: 25 Control Mean: 17 Control Standard Deviation: 4.19 (a) What is the PP-value for this test? (b) The conclusion is A. There is sufficient evidence to children at Montessori schools performed differently than children at other schools. B. There is not sufficient evidence to children at Montessori schools performed differently than children at other schools.

(a) .0546 (b) B. There is not sufficient evidence to children at Montessori schools performed differently than children at other schools. Explanation: 2-SampTTest in excel, use 2-tailed p-value

Do women talk more than men? Equip male and female students with a small device that records sound for a random thirty seconds during each 12.512.5-minute period over two days. Count the words each subject speaks during each recording period, and from this, estimate how many words per day each subject speaks. The published report includes a table summarizing the results. Women Sample Size: 27 Women Mean: 16496 Women Standard Deviation: 7914 Men Sample Size: 20 Men Mean: 12867 Men Standard Deviation: 8343 (a) What is the P-value for this test? (b) The conclusion is A. There is not sufficient evidence to conclude that women speak more words per day than men. B. There is sufficient evidence to conclude that women speak more words per day than men.

(a) .069 (b) B. There is sufficient evidence to conclude that women speak more words per day than men. Explanation: 2-SampTTest in excel, use 1-tailed p-value

Cuckoos lay their eggs in the nests of other (host) birds. The eggs are then adopted and hatched by the host birds. But the potential host birds lay eggs of different sizes. Does the cuckoo change the size of her eggs for different foster species? Lengths (in mm) of cuckoo eggs found in nests of sparrows and robins were recorded. [The data are drawn from the work of O.M. Latter in 1902 and were used in a fundamental testbook on statistical quality control by L.H.C. Tippett (1902-1985), one of the pioneers in that field.] A two-sample t test was performed in R, a popular statistical programming language. Does the R output indicate that there is evidence that cuckoo eggs are different in length when they are laid in sparrows' versus robins' nests? (a) What is the P-value for this test? (b) Using a significance level of 5%, the conclusion is A. There is not evidence to conclude that the egg lengths are different. B. There is evidence to conclude that the egg lengths are different.

(a) .1153 (b) A. There is not evidence to conclude that the egg lengths are different. Explanation: Answer in graphic

Suppose the number of households with children has a binomial distribution with parameters n = 21, and p = 85 %.Find the probability that the number of households with children is: (a) 8 or 20 (b) 18 or fewer (c) 10 or more (d) fewer than 20 (e) more than 18

(a) .1221 (b) .6295 (c) .999 (d) .8449 (e) .3704 Explanation: (a) X=8 or x=20 Binomialpdf (21, .85, 8) + Binomialpdf (21, .85, 8) (b) Binomialcdf (21, .85, 18) (c) 1 - Binomialcdf (21, .85, 10) (d) Binomialcdf (21, .85, 19) (e) Binomialcdf (21, .85, 18)

In a certain community, 20% of the families own a dog, and 20% of the families that own a dog also own a cat. It is also known that 25% of all the families own a cat. (a) What is the probability that a randomly selected family owns a dog? (b) What is the conditional probability that a randomly selected family owns a dog given that it owns a cat?

(a) .20 (b) .16 Explanation: see pic

Suppose that A and B are two independent events for which P(A)=0.27 and P(B)=0.61. Find each of the following: A. P(A|B)= B. P(B|A)= C. P(AandB)= D. P(AorB)=

(a) .27 (b) .61 (c) .1647 (d) .7153 Explanation: (a) conditional probability calculator (b) conditional probability calculator (c) Probability calculator (d) Probability calculator

The following table lists the joint probabilities associated with smoking and lung disease among 60-to-65 year-old men. One 60-to-65 year old man is selected at random. What is the probability of the following events? A. He is a smoker: B. He does not have lung disease: C. He has lung disease given that he is a smoker: D. He has lung disease given that he does not smoke:

(a) .28 (b) .85 (c) .393 (d) .0556 Explanation: (a) .11 +.17 (b) .17 +.68 (c) .11/.28 (total smoker) (d) .04/.72 (total nonsmoker)

You must decide which of two discrete distributions a random variable X has. The following table shows the probabilities that each distribution assigns to values of X. Value of X: 1, 2, 3, 4 Distribution 1: 0.7, 0.1 0.1, 0.1 Distribution 2: 0.1, 0.1, 0.3, 0.5 You have a single observation on X and you use it to test H0: Distribution 1 is correct Ha: Distribution 2 is correct You decide to reject H0 if X=2, 3, or 4. (a) What is the probability of a Type I error? (b) What is the probability of a Type II error?

(a) .3 (b) .1 Explanation: see pic

Two random samples are taken, one from among first-year students and the other from among fourth-year students at a public university. Both samples are asked if they favor modifying the student Honor Code. A summary of the sample sizes and number of each group answering "yes'' are given below: First-Years (Pop. 1): n1=86, x1=48 Fourth-Years (Pop. 2): n2=86, x2=46 Is there evidence, at an α=0.055 level of significance, to conclude that there is a difference in proportions between first-years and fourth-years? Carry out an appropriate hypothesis test, filling in the information requested. A. The value of the standardized test statistic: B. The PP-value is: C. Your decision for the hypothesis test: A. Do Not Reject H1. B. Reject H1. C. Do Not Reject H0. D. Reject H0.

(a) .30632 (b) .759 (c) C. Do Not Reject H0. Explanation: Use 2PropZTest in excel

Choose a student in grades 9 to 12 at random and ask if he or she is studying a language other than English. Here is the distribution of the students: (a) What is the probability that a randomly chosen student is, in fact, studying a language other than English? (b) What is the probability that a randomly chosen student is studying French, German, or Spanish? (c) What is the probability that a randomly chosen student is studying a language besides English, but not German?

(a) .39 (b) .38 (c) .37 Explanation: Add stuff

An automobile insurer has found that repair claims are Normally distributed with a mean of $650 and a standard deviation of $610. (a) Find the probability that a single claim, chosen at random, is less than $620. (b) Now suppose that the next 50 claims can be regarded as a random sample from the long-run claims process. Find the probability that the average x¯ of the 50 claims is smaller than $620. (c) If a sample larger than 50 claims is considered, there would be chance of getting a sample with an average smaller than $620.

(a) .4803 (b) .3640 (c) less Explanation: see pic

Shoppers can pay for their purchases with cash, a credit card, or a debit card. Suppose that the proprietor of a shop determines that 51% of her customers use a credit card, 25% pay with cash, and the rest use a debit card. (a) What is the probability that a customer does not use a credit card? (b) What is the probability that a customer pays in cash or with a credit card?

(a) .49 (b) .76 Explanation: (a) cash + debit (b) cash + credit

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score μμ of those who took the MCAT at Etown, you obtain a simple random sample of 23 students' scores. The scores follow a normal distribution, and from published information you know that the standard deviation is 6.46.4. Suppose that (unknown to you) the mean score of those taking the MCAT at Etown is 28. (a) If you choose one MCAT score at random, then what is the probability that the student's score is between 20 and 30? (b) What is the probability that the mean score of your sample is between 20 and 30?

(a) .5170 (b) .933024 Explanation: see pic

According to a recent marketing campaign, 130 drinkers of either Diet Coke or Diet Pepsi participated in a blind taste test to see which of the drinks was their favorite. In one Pepsi television commercial, an announcer states that "in recent blind taste tests, more than one half of the surveyed preferred Diet Pepsi over Diet Coke." Suppose that out of those 130, 68 preferred Diet Pepsi. Test the hypothesis, using α=0.01α=0.01 that more than half of all participants will select Diet Pepsi in a blind taste test by giving the following: (a) the test statistic (b) the P-value (c) The final conclusion is: A. We can reject the null hypothesis that p=0.5 and accept that p>0.5. B. There is not sufficient evidence to reject the null hypothesis that p=0.5.

(a) .526 (b) .299 (c) B. There is not sufficient evidence to reject the null hypothesis that p=0.5. Explanation: 1-PropZTest calc o N= 130 o X= 68 o Po= 1/2 o >

A poll is taken in which 318 out of 525 randomly selected voters indicated their preference for a certain candidate. (a) Find a 99% confidence interval for p. (b) Find the margin of error for this 99% confidence interval for p. (c) Without doing any calculations, indicate whether the margin of error is larger or smaller or the same for an 80% confidence interval. A. larger B. smaller C. same

(a) .5499 ≤ p ≤ .6598 (b) .05475 (c) B. smaller Explanation: 1-PropZInt Excel

If X is a binomial random variable with n and p as indicated, compute the probabilities for each of the following cases: (a) P(x≤4), n=8, p=0.4 (b) P(x>1), n=3, p=0.9 (c) P(x<5), n=8, p=0.6 (d) P(x≥1), n=3, p=0.5

(a) .8263 (b) .972 (c) .4059 (d) .875 Explanation: (a) binomialcdf (8, .4, 4) (b) 1 - binomialcdf (3, .9, 1) (c) binomialcdf (8, .6, 5) (d) P >= 1 turns into P<= 2 so 1 - binomialcdf (3, .5, 2)

The distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal with mean 88 ounces and standard deviation 0.12 ounces. (a) What is the probability that the average weight of a bar in a simple random sample of five of these chocolate bars is between 7.81 and 8.16 ounces? (b) For a simple random sample of five of these chocolate bars, what is the level L such that there is a 44% chance that the average weight is less than L?

(a) .9983 (b) 7.90 Explanation: see pic

Cocaine addiction is hard to break. Addicts need cocaine to feel any pleasure, so perhaps giving them an antidepressant drug will help. A three-year study with 72 chronic cocaine users compared an antidepressant drug called desipramine with lithium and a placebo. One third of the subjects, chosen at random, received each treatment. Use the SPSS output below to answer the following questions. (a) What is the P-value? (b) What is our conclusion? A. There is not sufficient evidence to conclude that frequency of relapse depends on the type of treatment. B. There is sufficient evidence to show that frequency of relapse depends on the type of treatment.

(a) 0.005247518 (b) B. There is sufficient evidence to show that frequency of relapse depends on the type of treatment. Explanation: Use Chi2 and df to find P-value in excel

The Wade Tract in Thomas County, Georgia, is an old-growth forest of longleaf pine trees (Pinus palustris) that has survived in a relatively undisturbed state since before the settlement of the area by Europeans. Foresters who study these trees are interested in how the trees are distributed in the forest. Are the locations of the trees random, or is there some sort of clustering? (See the figure below.) To answer this question, the tract is divided into four equal quadrants, in the east-west direction. Call the four quadrants Q1Q1, Q2Q2, Q3, and Q4. Then we take a random sample of 100100 trees and count the number of trees in each quadrant. The data are listed below. Perform the goodness-of-fit significance test for these data. (a) P-value: (b) If the significance level is 5%, what is our conclusion? A. There is not sufficient evidence to conclude that tree distributions are not uniformly random. B. There is sufficient evidence to conclude that tree distributions are not uniformly random.

(a) 0.012858001 (b) B. There is sufficient evidence to conclude that tree distributions are not uniformly random. Explanation: Goodness of Fit in excel

(Note that an Ace is considered a face card for this problem) In drawing a single card from a regular deck of 52 cards we have: (a) P( face card or a number card ) = (b) P( Queen and a 3 ) = (c) P( black or a 3 ) = (d) P( black or a face card ) = (e) P( black and a Queen ) =

(a) 1 (b) 0 (c) .538 (d) .654 (e) .0385 Explanation: (a) 100% (b) 0% (c) 26/52 + 2/52 (d) 26/52 + 8/52 (e) black queens: 2/52

Independent random samples, each containing 70 observations, were selected from two populations. The samples from populations 1 and 2 produced 22 and 16 successes, respectively. Test H0:p1=p2 against Ha:p1>p2. Use α=0.04. (a) The test statistic is: (b) The PP-value is: (c) The final conclusion is A. We can reject the null hypothesis that p1=p2 and accept that p1>p2. B. There is not sufficient evidence to reject the null hypothesis that p1=p2.

(a) 1.14 (b) .127 (c) B. There is not sufficient evidence to reject the null hypothesis that p1=p2. Explanation: Use 2PropZTest in excel

A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS of n=1200n=1200 registered voters and found that 620 would vote for the Republican candidate. Let pp represent the proportion of registered voters in the state who would vote for the Republican candidate. We test: H0:p=0.50 Ha:p>0.50 (a) What is the z-statistic for this test? (b) What is the P-value of the test?

(a) 1.154 (b) .124 Explanation: 1-PropZTest calc o N= 1200 o X= 620 o Po= .5 o >

A company sells sunscreen in 350 milliliter (ml) tubes. In fact, the amount of lotion in a tube varies according to a normal distribution with mean μ=348 ml and standard deviation σ=3 ml. Suppose a store which sells this sunscreen advertises a sale for 6 tubes for the price of 5. Consider the average amount of lotion from a SRS of 6 tubes of sunscreen and find: (a) The standard deviation of the average, x¯ : (b) The probability that the average amount of sunscreen from 6 tubes will be less than 342 ml.:

(a) 1.2247 (b) 0 Explanation: o 3/sqrt(6) o X < 342 = 1-normcdf (0, infinity, 348, 3/sqrt(6))

A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 70 women over the age of 50 used the new cream for 6 months. Of those 70 women, 35 of them reported skin improvement (as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 40% of women over the age of 50? Test using α=0.01. (a) Test statistic: (b) P-value= (c) The final conclusion is A. There is not sufficient evidence to reject the null hypothesis that p=0.4. That is, there is not sufficient evidence to reject that the cream can improve the skin of more than 40% of women over 50. B. We can reject the null hypothesis that p=0.4 and accept that p>0.4. That is, the cream can improve the skin of more than 40% of women over 50.

(a) 1.707 (b) .043 (c) A. There is not sufficient evidence to reject the null hypothesis that p=0.4. That is, there is not sufficient evidence to reject that the cream can improve the skin of more than 40% of women over 50. Explanation: 1-PropZTest calc o N= 70 o X= 35 o Po= .4 o >

Suppose a random variable xx is normally distributed with μ=17μ=17 and σ=5. According to the Central Limit Theorem, for samples of size 9: (a) The mean of the sampling distribution for x¯ is: (b) The standard deviation of the sampling distribution for x¯ is:

(a) 17 (b) 1.666 Explanation: o Xbar = mean o Sd = 5/sqrt(9)

Independent random samples, each containing 70 observations, were selected from two populations. The samples from populations 1 and 2 produced 27 and 16 successes, respectively. Test H0:p1=p2 against Ha:p1≠p2. Use α=0.1. (a) The test statistic is: (b) The PP-value is: (c) The final conclusion is A. We can reject the null hypothesis that p1=p2p1=p2 and accept that p1≠p2. B. There is not sufficient evidence to reject the null hypothesis that p1=p2.

(a) 2.015 (b) .0438 (c) A. We can reject the null hypothesis that p1=p2p1=p2 and accept that p1≠p2. Explanation: Use 2PropZTest in excel

One of the most feared predators in the ocean is the great white shark. It is known that the white shark grows to a mean length of 20 feet; however, one marine biologist believes that great white sharks off the Bermuda coast grow much longer. To test this claim, full-grown white sharks were captured, measured, and then set free. However, this was a difficult, costly and very dangerous task, so only four sharks were actually sampled. Their lengths were 22, 20, 21, and 24. Do the data provide sufficient evidence to support the claim? Use α=0.01. (a) Calculate the test statistic: t= (b) Compute the PP-value: (c) The final conclusion is A. There is not sufficient evidence to reject the null hypothesis that the average length of the shark is 20. B. We can reject the null hypothesis that the average length of the shark is 20.

(a) 2.049 (b) .066 (c) A. There is not sufficient evidence to reject the null hypothesis that the average length of the shark is 20. Explanation: T-test in Excel

Justin is interested in buying a digital phone. He visited 9 stores at random and recorded the price of the particular phone he wants. The sample of prices had a mean of 355.71 and a standard deviation of 31.82. (a) What value for t∗ should be used for a 95% confidence interval for the mean, μ, of the distribution? (b) Calculate a 95% confidence interval for the mean price of this model of digital phone:

(a) 2.306 (b) 331.25 < μ < 380.1690 Explanation: T-Interval in Excel

A noted psychic was tested for ESP. The psychic was presented with 240 cards face down and was asked to determine if the card was one of 5 symbols: a star, cross, circle, square, or three wavy lines. The psychic was correct in 65 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. Assume the 240 trials can be treated as an SRS from the population of all guesses.To see if there is evidence that the psychic is doing better than just guessing, we test: H0:p=0.2 Ha:p>0.2 (a) What is the z-statistic for this test? (b) What is the P-value of the test?

(a) 2.743 (b) .003 Explanation: 1-PropZTest calc o N= 240 o X= 65 o Po= .2 o >

The number of men and women among professors in Math, Physics, Chemistry, Linguistics, and English departments from a simple random sample of small colleges were counted, and the results are shown in the table below. Test the claim that the gender of a professor is independent of the department. Use the significance levelα=0.01. (a) χ2= (b) P-value = (c) Is there sufficient evidence to warrant the rejection of the claim that the gender of a professor is independent of the department? A. Yes B. No

(a) 21.80894683 (b) 0.000218755 (c) A. Yes Explanation: X-2Test in Excel

It has been suggested that the highest priority of retirees is travel. Thus, a study was conducted to investigate the differences in the length of stay of a trip for pre-and post-retirees. A sample of 680 travelers were asked how long they stayed on a typical trip. The observed results of the study are found below. Construct a table of estimated expected values. (a) χ2= (b) Degrees of freedom= (c) P-value = (d) The final conclusion is A. We can reject the null hypothesis that the length of stay is independent of retirement and accept the alternative hypothesis that the two are dependent. B. There is not sufficient evidence to reject the null hypothesis that the length of stay is independent of retirement.

(a) 25.54454465 (b) 3 (c) .000018 (d) A. We can reject the null hypothesis that the length of stay is independent of retirement and accept the alternative hypothesis that the two are dependent. Explanation: X-2Test in Excel

The level of nitrogen oxides (NOX) in the exhaust of a particular car model varies with mean 0.9 grams per mile and standard deviation 0.2 grams per mile . (a) What sample size is needed so that the standard deviation of the sampling distribution is 0.01 grams per mile (b) If a smaller sample is considered, the standard deviation for x¯ would be

(a) 400 (b) larger Explanation o A: (pic) o B: Smaller sample, larger sd and vice versa

A certain health maintenance organization (HMO) wishes to study why patients leave the HMO. A simple random sample of 372372 patients was taken. Data were collected on whether a patient had filed a complaint and, if so, whether the complaint was medical or nonmedical in nature. After a year, a tally from these patients was collected to count number who left the HMO voluntarily. Here are the data on the total number in each group and the number who voluntarily left the HMO: If the null hypothesis is H0:p1=p2=p3H0:p1=p2=p3 and using α=0.05, then do the following: (a) Find the expected number of people with no complaint who leave the HMO: (b) Find the expected number of people with a medical complaint who leave the HMO: (c) Find the expected number of people with a nonmedical complaint who leave the HMO: (d) Find the test statistic: (e) Find the degrees of freedom: (f) Find the PP-value: (g) The final conclusion is A. There is not sufficient evidence to reject the null hypothesis. B. We can reject the null hypothesis that the proportions are equal.

(a) 48 (b) 24 (c) 52 (d) 2.502403846 (e) 2 (f) 0.286160647 (g) A. There is not sufficient evidence to reject the null hypothesis. Explanation: X-2Test in Excel, find what adds up to total (41 +103 =144)

Consider the population of four juvenile condors. Their weights in pounds are : 5, 6, 9, 13 (a) Let xx be the weight of a juvenile condor. Write the possible unique values for xx: (b) Find the mean of the population: (c) Let x¯ be the average weight from a sample of two juvenile condors. List all possible outcomes for x¯. (If a value occurs twice, make sure to list it twice.) This is the sampling distribution for samples of size 2: (d) Find the mean of the sampling distribution:

(a) 5, 6, 9, 13 (b) 8.25 (c) 5.5, 7, 9, 7.5, 9.5, 11 (d) 8.25 Explanation: o A: all numbers o B: mean of values o C: 5x6, 5x9, 5x13, 6x9, 6x13, 9x13 o D: mean of values of C

Test the claim that the two samples described below come from populations with the same mean. Assume that the samples are independent simple random samples. Sample 1: n1=20, x¯1=19, s1=2.5. Sample 2: n2=10, x¯2=12, s2=4. (a) The test statistic is: (b) Find the P-value for an alternative hypothesis that the first population has a larger mean: (c) The conclusion is A. There is not sufficient evidence to warrant rejection of the claim that the two populations have the same mean. B. There is sufficient evidence to warrant rejection of the claim that the two populations have the same mean and accept that the first population has a larger mean.

(a) 5.06 (b) .0001 (c) B. There is sufficient evidence to warrant rejection of the claim that the two populations have the same mean and accept that the first population has a larger mean. Explanation: 2-SampTTest in excel

Real estate ads suggest that 58% of homes for sale have garages, 41% have swimming pools, and 38% have both features. What is the probability that a home for sale: (a) has a pool or a garage? (b) neither a pool nor a garage? (c) a pool but no garage?

(a) 61% (b) 39% (c) 3% Explanation: (a) 58% + 41% - 38% (b) ? (c) 41% - 38% = 3%

Suppose you needed to test the claim that the two samples described below come from populations with the same mean. Assume that the samples are independent simple random samples. Sample 1: n1=14, x¯1=27.8, s1=3.84 Sample 2: n2=7, x¯2=25.5, s2=8.04 Compute: (a) the degrees of freedom: (b) the test statistic (use Sample 1 −− Sample 2): (c) the P-value:

(a) 7.4022 (b) .717 (c) .49 Explanation: 2-SampTTest in excel

Suppose a group of 900 smokers (who all wanted to give up smoking) were randomly assigned to receive an antidepressant drug or a placebo for six weeks. Of the 483 patients who received the antidepressant drug, 184 were not smoking one year later. Of the 417 patients who received the placebo, 66 were not smoking one year later. Given the null hypothesis: H0: p(drug)=p(placebo) and the alternative hypothesis Ha:p(drug)≠p(placebo), conduct a test to see if taking an antidepressant drug can help smokers stop smoking. Use α=0.02. (a) The test statistic is: (b) The PP-value is: (c) The final conclusion is A. There is not sufficient evidence to determine whether the antidepressant drug had an effect on changing smoking habits after one year. B. There is strong evidence that the patients taking the antidepressant drug have a different success rate of not smoking after one year than the placebo group.

(a) 7.437 (b) .000000000000102 (c) B. There is strong evidence that the patients taking the antidepressant drug have a different success rate of not smoking after one year than the placebo group. Explanation: Use 2PropZTest in excel

1. (a) The mean is closest to: (b) The median is closest to: (c) Is this data skewed to the right, symmetric, or skewed to the left?

(a) A (b) B (c) skewed left Explanation: In left-skewed data (tail is at the left), the mean is closest to the tail (to the left) and the mode is at the tallest point (c), leaving the median to be B

(a) A test with hypotheses H0:μ=5, Ha:μ<5, sample size 36, and assumed population standard deviation 1.2 will reject H0 when x¯<4.67. What is the power of this test against the alternative μ=4.5? A. 0.8023 B. 0.5715 C. 0.9993 D. 0.1977 (b) A test with hypotheses H0:μ=500,Ha:μ>500, sample size 64, and assumed population standard deviation 25 will reject H0 when x¯>505.14. What is the power of this test against the alternative μ=510? A. 0.94 B. 0.06 C. 0.58 D. 0.42

(a) A. 0.8023 (b) A. 0.94 Explanation: see pic

(a) Scores on the mathematics part of the SAT exam in a recent year were roughly Normal with mean 551 and standard deviation 119. You choose an SRS of 100 students and average their SAT math scores. If you do this many times, with a sample of size 100 each time, the mean of the average scores will get close to A. 551 B. 5.51 C. 55.1 D. None of the above. (b) A newborn baby has extremely low birth weight (ELBW) if it weighs less than 1000 grams. A study of the health of such children in later years examined a random sample of 219 children. Their mean weight at birth was x¯= 810 grams. This sample mean is an unbiased estimator of the mean weight μ in the population of all ELBW babies. This means that A. the sample mean x¯ will have a distribution that is close to Normal. B. the sample mean x¯ is always equal to μ. C. the average sample mean x¯, over all possible samples, is equal to μ. D. None of the above. (c) The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. The probability that the average pregnancy length for 6 randomly chosen women exceeds 270 days is about A. 0.07 B. 0.4 C. 0.27 D. None of the above.

(a) A. 551 (b) C. the average sample mean x¯, over all possible samples, is equal to μ. (c) C. 0.27 Explanation o A: Same as mean in problem o B: means are equal to each other o C: (pic)

Below is a bar graph of class standing for a Finance seminar containing five students who are either freshman, sophomores, juniors, or seniors. In the bar graph the bar for the juniors has been omitted. (a) The percentage of students in the seminar who are not juniors is A. 80% B. 20% C. 40% D. 60% E. None of the above. (b) The number of students in the seminar who are juniors is _____

(a) A. 80% (b) 1 Explanation: (a) Since there are 5 students are 4 are shown on the graph now, then 80% are not juniors (b) There are 5 students but only 4 shown in the graph

Ten randomly selected people took IQ test A, and next day they took a very similar IQ test B. Their scores are shown in the table below. Person: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Test A: 90, 100, 121, 95, 84, 104, 72, 108, 116, 101 Test B: 88, 99, 120, 99, 85, 104, 75, 108, 112, 104 Consider (Test A −− Test B). Use a 0.05 significance level to test the claim that people do better on the second test than they do on the first. (a) What test method should be used? A. Matched Pairs B. Two Sample p C. Two Sample t (b) The test statistic is (c) The P-value is (d) Is there sufficient evidence to support the claim that people do better on the second test? A. Yes B. No (e) Construct a 9595% confidence interval for the mean of the differences. Again, use (Test A −− Test B).

(a) A. Matched Pairs (b) -0.379980298 (c) 0.356385901 (d) B. No (e) -2.0860 < μ < 1.4860 Explanation: T-Test in Excel using differences

The University of Michigan Health and Retirement Study (HRS) surveys more than 22,000 Americans over the age of 50 every two years. A subsample of the HRS participated in the 2009 Internet-based survey that collected information on a number of topical areas, including health, psychosocial items, economics, and retirement. Two of the questions asked on the Internet survey were "Would you say your health is excellent, very good, good, fair, or poor?" and "Do you smoke cigarettes now?" The R programming language produced the results shown below. What is conclusion does the analysis suggest? A. There is sufficient evidence to show that the self-evaluation of health is dependent on smoker status. B. There is insufficient evidence to show that the self-evaluation of health is dependent of smoker status.

(a) A. There is sufficient evidence to show that the self-evaluation of health is dependent on smoker status. Explanation: Look at p-value to assess

2. (a) The mean is closest to: (b) The median is closest to: (c) Is this data skewed to the right, symmetric, or skewed to the left?

(a) B (b) B (c) Symmetric Explanation: The data is symmetric so the mean, median, and mode would all be closest to the middle mark

(a) Type I error is: A. Deciding the null hypothesis is true when it is false B. Deciding the null hypothesis is false when it is true C. Deciding the alternative hypothesis is true when it is true D. Deciding the alternative hypothesis is true when it is false E. All of the above F. None of the above (b) Type II error is: A. Deciding the null hypothesis is true when it is false B. Deciding the alternative hypothesis is false when it is true C. Deciding the null hypothesis is false when it is true D. Deciding the alternative hypothesis is true when it is true E. All of the above F. None of the above

(a) B. Deciding the null hypothesis is false when it is true (b) A. Deciding the null hypothesis is true when it is false

(a) In drawing a histogram, which of the following suggestions should be followed? A. The scale of the vertical axis should be that of the variable whose distribution you are displaying. B. The heights of bars should equal the class frequency. C. Leave large gaps between bars. This allows room for comments. D. Generally, bars should be square so that both the height and width equal the class count. (b) When drawing a histogram it is important to A. make sure the heights of the bars exceed the widths of the class intervals so that the bars are true rectangles. B. have a separate class interval for each observation to get the most informative plot. C. make certain the mean and median are contained in the same class interval, so that the correct type of skewness can be identified. D. label the vertical axis so the reader can determine the counts or percent in each class interval. E. None of the above.

(a) B. The heights of bars should equal the class frequency. (b) D. label the vertical axis so the reader can determine the counts or percent in each class interval.

(a) A description of different houses on the market includes the following three variables. Which of the variables is quantitative? A. The exterior paint colors. B. The monthly electric bill. C. The street number. D. The school district. E. None of the above. (b) A survey records many variables of interest to the researchers conducting the survey. Below are some of the variables from a survey conducted by the U.S. Postal Service. Which of the variables is categorical? A. Number of people, both adults and children, living in the household. B. Total household income, before taxes, in 1993. C. Age of respondent. D. County of residence. E. None of the above. (c) A description of different houses on the market includes the following three variables. Which of the variables is quantitative? A. The exterior paint colors. B. The monthly electric bill. C. The street number. D. The school district. E. None of the above.

(a) B. The monthly electric bill. (b) D. County of residence. (c) B. The monthly electric bill. Explanation: (a) Quantitative variables are numerical (b) All of the other responses are numerical

The timeplot below gives the share price in dollars of General Electric stock, with the bar chart giving the volume in millions of shares. The plots are for the one-year period September 2001-September 2002. (a) Which of the following is a true statement? A. There has been a general upward trend in the stock price over this time period. B. There has been a general downward trend in the stock price over this time period. C. The price should return to 40 dollars within six months because of the cycle. D. The price of General Electric stock has been stable for this year. E. None of the above. (b) The maximum price per share for this time period was about A. 20 dollars. B. 25 dollars. C. 41 dollars. D. 45 dollars. E. None of the above. (c) If you bought a single share of stock at the maximum price and sold it at the minimum price during this one-year period, you would have lost about A. 15 dollars. B. 45 dollars. C. 35 dollars. D. 25 dollars. E. Cannot be determined from the graph.

(a) B. There has been a general downward trend in the stock price over this time period. (b) A. 20 dollars. (c) C. 35 dollars. Explanation: (a) The line is going down (b) the peak of the line is at about 41 (c) Max= 41, Min = 25, so it is about a 15-dollar difference

For a Physics course containing 10 students, the maximum point total for the quarter was 200. The point totals for the 10 students are given in the stemplot below. (a) This stemplot is most similar to A. a time plot of the data with the observations taken in increasing order. B. a histogram with class intervals between 110 and 120, between 120 and 130, etc. C. reporting the 5-point summary for the data, with the mean. D. a boxplot of the data. E. None of the above. (b) To which of the following data sets does this stemplot correspond? A. 116, 118, 121, 124, 128, 133, 137, 142, 146, 179 B. 1, 2, 3, 4, 6, 6, 7, 8, 8, 9 C. 16, 18, 21, 24, 28, 33, 37, 42, 46, 79 D. all integers between 116 and 179 (c) The lowest score in the class as a percentage of the total possible points is ________%

(a) B. a histogram with class intervals between 110 and 120, between 120 and 130, etc. (b) A. 116, 118, 121, 124, 128, 133, 137, 142, 146, 179 (c) 58% Explanation: (a) Stemplots are similar to histograms (b) These numbers match the stem and leaves (c) Lowest values divided by 2 to make the data out of 100 (116/200 = 58/100)

(a) The probability of a Type I error is denoted by: A. 1−β B. α C. β D. 1−α (b) The power of a test is the probability that it will lead us to: A. fail to reject the null hypothesis when it is true B. reject the null hypothesis when it is true C. reject the null hypothesis when it is false D. fail to reject the null hypothesis when it is false

(a) B. α (b) C. reject the null hypothesis when it is false

(a) Here are the amounts of money (cents) in coins carried by 10 students in a statistics class: 50 35 0 97 76 0 0 87 23 65 To make a stemplot of these data, you would use stems A. 0, 2, 3, 5, 6, 7, 8, 9. B. 00, 10, 20, 30, 40, 50, 60, 70, 80, 90. C. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. D. None of the above. (b) To display the distribution of grades (A, B, C, D, F) in a course, it would be correct to use A. either a pie chart or a bar graph. B. a pie chart but not a bar graph. C. a bar graph but not a pie chart. D. None of the above. (c) A political party's data bank includes the zip codes of past donors, such as 47906 34236 53075 10010 90210 75204 30304 99709 Zip code is a A.Quantitative variable. B.Unit of Measurement. C.Categorical variable. D.None of the above.

(a) C. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. (b) A. either a pie chart or a bar graph. (c) C.Categorical variable. Explanation: (a) Must use all numbers for stems, even if there are gaps (b) Anything with this type of variable that is a pie chart can be a bar graph and vice versa (c) Categorical variables are not numerical and describe something

Suppose that math SAT (SATM) scores vary normally with mean μ=515. After several sessions with an SATM coaching service, 5000 students had an average SATM of 518 with standard deviation 92.1. Consider the significance test H0:μ=515 Ha:μ>515 (a) What is the PP-value for the test? A. 0.1182 B. 0.0003 C. 0.01065 D. 0.0984 (b) Give a 95% confidence interval for μ. A. (337.4,698.6)(337.4,698.6) B. (515.4,520.6)(515.4,520.6) C. (423.6,523.6)(423.6,523.6) D. (502.9,527.1)(502.9,527.1) (c) Choose the best answer. A. There is no statistical evidence to show that SATM coaching is effective. B. The confidence interval is so large that it makes the results difficult to interpret. C. Although the coaching appears to have a statistically significant effect on student SATM scores, the effect is too small to be practically significant. D. Since the PP-value is less than 0.050.05, we have strong evidence that SATM coaching is effective.

(a) C. 0.01065 (b) B. (515.4,520.6)(515.4,520.6) (c) C. Although the coaching appears to have a statistically significant effect on student SATM scores, the effect is too small to be practically significant. Explanation: T-Interval and T-test in excel

Consumers Union measured the gas mileage in miles per gallon of 38 1978-79 model automobiles on a special test track. The pie chart below provides information about the country of manufacture of the model cars used by Consumers Union. (a) Based on this pie chart, we may conclude that A. Japanese cars get significantly lower gas mileage than cars of other countries. This is because their slice of the pie is at the bottom of the chart. B. Mercedes Benz, Audi, Porsche, and BMW represent approximately one quarter of the cars tested. C. more than half of the cars in the study were from the United States. D. Swedish cars get gas mileages that are between those of Japanese and American cars. E. None of the above. (b) The information displayed in the pie chart can also be displayed in a A. bar chart. B. scatter plot. C. timeplot. D. histogram. E. None of the above.

(a) C. more than half of the cars in the study were from the United States. (b) A. bar chart. Explanation: (a) (b) Pie charts can also be bar charts

(a)Statisticians can translate PP-values into several descriptive terms. Which of the following statements are correct? A. if 0.01<P-value<0.050.01<P-value<0.05 there is strong evidence to infer that the alternative hypothesis is true B. if 0.05<P-value<0.100.05<P-value<0.10, there is weak evidence to infer that the alternative hypothesis is true C. if the P-value<0.01P-value<0.01, there is overwhelming evidence to infer that the alternative hypothesis is true D. All of the above statements are correct (b) In a two-tail test for the population mean, if the null hypothesis is rejected when the alternative hypothesis is true, A. a Type I error is made B. a correct decision is made C. a Type II error is made D. a one-tail test should be used instead of a two-tail test

(a) D. All of the above statements are correct (b) B. a correct decision is made

(a) Which of the following is a correct statement? A. Approximately half the students have heights between 65 and 71 inches. B. The tallest person must have a height of at least 79 inches. C. The histogram is symmetric. D. None of the above are correct. (b) The interval that contains closest to 10 students is A. 74-80 inches. B. 56-68 inches. C. 68-71 inches. D. 59-65 inches. E. None of the above.

(a) D. None of the above are correct. (b) C. 68-71 inches. Explanation: (a) (b) This category is closest to the frequency of 10

Recent revenue shortfalls in a southern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 20%20% tuition increase. It was determined that such a large increase was needed to simply compensate for lost support from the state. Random samples of 100100 freshmen, 100100 sophomores, 100100 juniors, and 100100 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the universityÃ¢ÂÂ's budget at current levels. The results are given in the following table. (a) To compare the four classes (freshman, sophomore, junior, senior) with respect to their opinion regarding the proposed tuition increase, which distribution should we calculate? A. the joint distribution of year in school and opinion B. the marginal distribution of year in school C. the conditional distribution of year in school given opinion D. the conditional distribution of opinion given year in school (b) Which hypotheses are being tested by the chi-square test? A. The null hypothesis is that the distributions of the total number of students sampled in each of the four years are the same. The alternative is that these distributions are different. B. The null hypothesis is that the mean number of students who are strongly opposed is the same for each of the four years, and the alternative is that these means are different. C. The null hypothesis is that the year in school and whether a student is strongly opposed are independent, and the alternative is that they are dependent. D. The null hypothesis is that the distributions of the number who are strongly opposed versus not strongly opposed are the same for the four years. The alternative says that these distributions are different.

(a) D. the conditional distribution of opinion given year in school (b) C. The null hypothesis is that the year in school and whether a student is strongly opposed are independent, and the alternative is that they are dependent.

(a) If a hypothesis is not rejected at the 0.10 level of significance, it: A. will not be rejected at the 0.20 level B. must be rejected at the 0.025 level C. must be rejected at the 0.05 level D. will not be rejected at the 0.05 level (b) The power of a test is the probability of making: A. an incorrect decision when the null hypothesis is true B. an incorrect decision when the null hypothesis is false C. a correct decision when the null hypothesis is true D. a correct decision when the null hypothesis is false

(a) D. will not be rejected at the 0.05 level (b) D. a correct decision when the null hypothesis is false

Suppose a couple planned to have three children. Let X be the number of girls the couple has. (a) List all possible arrangements of girls and boys. For example, if the couple had 2 girls and then a boy, then type GGB. (Separate each item in your list with a comma.): (b) List the sample space for X. (i.e. List the possible values that X may take separated by commas.): (c) What is the probability that X=1? (d) Find the probability that the couple have three boys:

(a) GGG, GGB, GBG, GBB, BBB, BGG, BGB, BBG (b) 3, 2, 1, 0 (c) .375 (d) .125 Explanation: (a) all numbers (b) All possible values of x would 3, 2, 1, 0 (c) 2/8 = .375 (d) 1/8 = .125

An agricultural field trial compares the yield of two varieties of corn. The researchers divide in half each of 1818 fields of land in different locations and plant each corn variety in one half of each plot. After harvest, the yields are compared in bushels per acre at each location. The 1818 differences (Variety A −− Variety B) give x¯=3.66 and s=2.37. Does this sample provide evidence that Variety A had a higher yield than Variety B? (a) State the null and alternative hypotheses: (b) Find the test statistic, t= (c) Does this sample provide evidence that Variety A had a higher yield than Variety B? (Use a 5% level of significance)

(a) H0: mu = 0 Ha: mu > 0 (b) 6.5519 (c) Yes Explanation: T-Test in excel

The hemoglobin count (HC) in grams per 100 milliliters of whole blood is approximately normally distributed with a population mean of 14 for healthy adult women. Suppose a female patient has had 1616 laboratory blood tests during the past year and her average HC is 15.215.2 with s=2.98. Is there evidence that her average HC is not 1414? (a) State the null and alternative hypotheses: (b) Find the test statistic, t= (c) Is there evidence that her average HC is not 14? (Use a 11% level of significance)

(a) H0: mu = 14 Ha: mu not = 14 (b) 1.6107 (c) No Explanation: T-test in Excel

Sam thinks that there is a difference in quality of life between rural and urban living. He collects information from obituaries in newspapers from urban and rural towns in Idaho to see if there is a difference in life expectancy. A sample of 1818 people from rural towns give a life expectancy of x¯r=75.7 years with a standard deviation of sr=8.72 years. A sample of 12 people from larger towns give x¯u=82.3 years and su=5.18 years. Does this provide evidence that people living in rural Idaho communities have different average life expectancy than those in more urban communities? Use a 10% level of significance. (a) State the null and alternative hypotheses. (b) The degrees of freedom is (c) The test statistic is (d) Based on this data, Sam concludes: A. There is not sufficient evidence to show that life expectancies are different for rural and urban communities. B. The results are significant. The data seems to indicate that people living in rural communities have a different life expectancy than those in urban communities.

(a) H0: mu_r = mu_u Ha: mu_r not = mu_u (b) 27.7458 (c) -2.596657111 (d) B. The results are significant. The data seems to indicate that people living in rural communities have a different life expectancy than those in urban communities. Explanation: 2-SampTTest in excel

Albert thinks that he has a special relationship with the number 5. In particular, Albert thinks that he would roll a 5 with a fair 6-sided die more often than you'd expect by chance alone. Suppose pp is the true proportion of the time Albert will roll a 5. (a) State the null and alternative hypotheses for testing Albert's claim. (b) Now suppose Albert makes n= 34 rolls, and a 5 comes up 7 times out of the 34 rolls. Determine the P-value of the test: (c) Answer the question: Does this sample provide evidence at the 5 percent level that Albert rolls a 5 more often than you'd expect?

(a) H0= p = 1/6 Ha = p > 1/6 (b) .2697 (c) No Explanation: 1-PropZTest calc o N= 34 o X= 7 o Po= 1/6 o >

The length, X, of a fish from a particular mountain lake in Idaho is normally distributed with μ=7.9 inches and σ=1.9 inches. (a) Is X a discrete or continuous random variable? (b) Write the event ''a fish chosen has a length equal to 4.9 inches'' in terms of X: . (c) Find the probability of this event: (d) Find the probability that the length of a chosen fish was greater than 9.9 inches: . (e) Find the probability that the length of a chosen fish was between 4.9 and 9.9 inches:

(a) continuous (b) x = 4.9 (c) 0 (d) .146 (e) .797 Explanation: (a) Fish can be any length, so continuous (b) x = the number of inches (c) probability = is always 0 (d) Excel: 1-norm.dist(value, mean, sd, true), greater than cause norm.dist always gives you less than (e) Excel: 1- norm.dist of both

Let the random variable X be the number of rooms in a randomly chosen owner-occupied housing unit in a certain city. The distribution for the units is given below. (a) Is X a discrete or continuous random variable? (b) What must be the probability of choosing a unit with 10 rooms? P(X=10) = _______ (c) What is the probability that a unit chosen at random has less than five rooms? P(X<5) = _____ (d) What is the probability that a unit chosen at random has three rooms? P(X=3) = ______ (e) What is the probability that a unit chosen at random has more than 5 rooms? P(X>5) = _______

(a) discrete (b) .01 (c) .27 (d) .06 (e) .29 Explanation: (a) There is a limited number of options, making it discrete (b) Add until = 100 (c) Add up values under 5 (d) Add up values = 3 (e) Add up values over 5

A study on the length of time a person brushes their teeth is conducted on a large population of adults. The mean brushing time is μ and the standard deviation is σ. A simple random sample of 160 adults is considered. (a) The mean of the sampling distribution is _____ the mean of the population. (b) The standard deviation of the sampling distribution is ______ the standard deviation of the population.

(a) equal to (b) less than Explanation o Means are equal to each other o Sd is always less

In a study of red/green color blindness, 550 men and 2500 women are randomly selected and tested. Among the men, 50 have red/green color blindness. Among the women, 5 have red/green color blindness. Test the claim that men have a higher rate of red/green color blindness. (a) State the null hypothesis: (b) State the alternative hypothesis: (c) The test statistic is (d) Is there sufficient evidence to support the claim that men have a higher rate of red/green color blindness than women? Use a 1 % significance level. A. Yes B. No (e) Construct the 99% confidence interval for the difference between the color blindness rates of men and women.

(a) p_m = p_w (b) p_m > p_w (c) 14.18 (d) A. Yes (e) .058145 <(pm−pw)< .12184 Explanation: Use both 2-Test and 2-Int Excel calculator

Scrapie is a degenerative disease of the nervous system. A study of the substance IDX as a treatment for scrapie used as subjects 28 infected hamsters. Fourteen, chosen at random, were injected with IDX. The other 1414 were untreated. The researchers recorded how long each hamster lived. They reported: "Thus, although all infected control hamsters had died by 93 days after infection (mean±SEM=86.5±1.71), IDX-treated hamsters lived up to 118 days (mean±SEM=108.4±2.57)." Note that SEM stands for the standard error of the mean, so the researchers are not reporting confidence intervals. (a) For the group injected with IDX, find: the mean, x¯= the standard deviation, s = (b) For the untreated group, find: the mean, x¯= the standard deviation, s =

(a) x¯= 108.4, s = 9.616 (b) x¯= 86.5, s = 6.398 Explanation: see pic

Is the number of games won by a major league baseball team in a season related to the team batting average? The table below shows the number of games won and the batting average (in thousandths) of 8 teams. The correlation coefficient is r= ________ The equation of the least squares line is ŷ = _____

-.075, 274.003 + -.035x Explanation: Correlation coefficient is found on the calculator, least squares is the equation

-2.869 + .183x Explanation: Calculator

Heights (in centimeters) and weights (in kilograms) of 77 supermodels are given below. Find the regression equation, letting the first variable be the independent (x)(x) variable, and predict the weight of a supermodel who is 171171 cm tall. The regression equation is ŷ = _____ + _____x. The best predicted weight of a supermodel who is 171 cm tall is _____

-88.033, .818, 51.7807 Explanation: Do slope equation for the first two, then plug in numbers for the last part

Use the Normal Approximation to the Binomial Distribution to compute the probability of passing a true/false test of 40 questions if the minimum passing grade is 90% and all responses are random guesses.

.000000210 Explanation: see pic

An airline company is considering a new policy of booking as many as 239 persons on an airplane that can seat only 230. (Past studies have revealed that only 88% of the booked passengers actually arrive for the flight.) Compute the probability that if the company books 239 persons. not enough seats will be available.

.00000199 Explanation: see pic

Find the probability of throwing a sum of 8 at least 8 times in 10 throws of a pair of fair dice.

.000004788 Explanation: P = 5/36 chances to get sum 8 N = 10 X >= 8 x <= 7 1 - binomialcdf

Subjects with preexisting cardiovascular symptoms who were receiving subitramine, an appetite suppressant, were found to be at increased risk of cardiovascular events while taking the drug. The study included 9804 overweight or obese subjects with preexisting cardiovascular disease and/or type 2 diabetes. The subjects were randomly assigned to subitramine (4906 subjects) or a placebo (4898 subjects) in a double-blind fashion. The primary outcome measured was the occurrence of any of the following events: nonfatal myocardial infarction or stroke, resuscitation after cardiac arrest, or cardiovascular death. The primary outcome was observed in 561 subjects in the subitramine group and 490 subjects in the placebo group. Give a 95% confidence interval for the difference between the proportions of subitramine and placebo subjects who experienced the primary outcome.

.00205 < p(subitramine) − p(placebo) < .02655

In 2012, the percentage of cell phone owners who used their cell phone to send or receive text messages was 80%. A polling firm contacted a simple random sample of 1100 people chosen from the population of cell phone owners. If p is the proportion of cell phone owners who used their phone to text, then what was the standard deviation for p̂ ?

.012 Explanation: sqrt .8(.2)/1100

In a study of retention rates of those using the Platinum Program at Jenny Craig in May 2001-May 2002, it was found that about 25% of those who began the program dropped out in the first four weeks. If we have a random sample of 251 people at the beginning of the program, what is the probability that at least 201 people in the sample will still be in the Platinum Program after the first four weeks?

.037 Explanation: Normalcdf (200.5, 251, 188.25 (251 - np), 6.8602)

.0858 Explanation:

Empathy means being able to understand what others feel. To see how the brain expresses empathy, researchers recruited 16 couples in their mid twenties who were married or had been dating for at least two years. They zapped the man's hand with an electrode while the woman watched, and measured the activity in several parts of the woman's brain that would respond to her own pain. Brain activity was recorded as a fraction of the activity observed when the woman herself was zapped with the electrode. The women also completed a psychological test that measures empathy. Given that the equation for the regression line is ŷ =0.00567x+0.03212, what is the residual for subject 16?

.119 Explanation: Observed value - predicted value = residual

Whooping cough (pertussis) is a highly contagious bacterial infection that was a major cause of childhood deaths before the development of vaccines. About 80% of unvaccinated children who are exposed to whooping cough will develop the infection, as opposed to only about 5% of vaccinated children.A group of 4 vaccinated children at a nursery school are exposed to whooping cough by playing with an infected child. What is the probability that at least one of the 4 children develop an infection?

.1854 Explanation: N = 4 P = .05 X >= 1 = x < 0 1- binomialcdf

Approximately 20% of cars in the United States are white. You take a simple random sample of 140 cars on Etown's campus and find that 36 are white. What is the proportion p̂ of white cars on Etown's campus?

.257 Explanation: binomialcdf

Genetic influences on cancer can be studied by manipulating the genetic makeup of mice. One of the processes that turns genes on or off (so to speak) in particular locations is called "DNA methylation". Of 33 mice with lowered levels of DNA methylation, 23 developed tumors. None of the control group of 18 normal mice developed tumors in the same time period. Give a 99% confidence interval for the difference in the proportions of the two populations that develop tumors.

.39778 < p1 − p2 < .87364 Explanation: Use 2PropZTest in excel

Approximately 20% of cars in the United States are white. You take a simple random sample of 200 cars on Etown's campus and find that 40 are white. If 20% of cars on Etown's campus are white, then what proportion of samples like yours would have 40 or fewer white cars?

In 2012, the percentage of cell phone owners who used their cell phone to send or receive text messages was 80%. A polling firm contacted a simple random sample of 2000 people chosen from the population of cell phone owners. If p is the proportion of cell phone owners who used their phone to text, then what was the the probability that p̂ was between 0.79 and 0.81?

.736

A basketball player makes 190 out of 240 free throws. We would estimate the probability that the player makes the next free throw to be _____

.7917 Explanation: 190/240

In 2012, the percentage of cell phone owners who used their cell phone to send or receive text messages was 80%. A polling firm contacted a simple random sample of 1900 people chosen from the population of cell phone owners. If p is the proportion of cell phone owners who used their phone to text, then what was the mean for p̂ ?

.80 Explanation: p

Whooping cough (pertussis) is a highly contagious bacterial infection that was a major cause of childhood deaths before the development of vaccines. About 80% of unvaccinated children who are exposed to whooping cough will develop the infection, as opposed to only about 5% of vaccinated children. A group of 23 vaccinated children at a nursery school are exposed to whooping cough by playing with an infected child. What is the probability that no more than 3 of the 23 children develop infections?

.974 Explanation: Binomialcdf (23, .05, 3)

Greeks bucked a global trend in which people in most countries expect their lives in five years to be better than their current lives. Even among those countries with much lower current life ratings, greater optimism was found because people cannot fathom their lives getting worse. But in Greece, only 25% expect their lives to be better in five years. In a simple random sample of 1800 Greek citizens, what is the probability that less than 28 percent of the sample expect their lives to be better in five years?

.9984

A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled " The relation of dive duration (DD) to depth (D)." Duration DD is measured in minutes and depth D is in meters. The report then says, " The regression equation for this bird is: DD = 2.15 + 0.0053 D. What is the slope of the regression line?

0.0053 minutes per meter Explanation: Plug in the 400-meter dive into the equation to get how many minutes the dive took

Select True or False from each pull-down menu, depending on whether the corresponding statement is true or false. 1. If we reject the null hypothesis, then we conclude that there is enough statistical evidence to infer that the alternative hypothesis is true. 2. The probability of making a Type I error and the level of significance are the same. 3. In a criminal trial, a Type I error is made when an innocent person is convicted. 4. The PP-value of a test is the smallest αα for which the null hypothesis can be rejected.

1. True 2. True 3. True 4. True

A random sample of 654 women aged 20 to 29 had a mean body mass index (BMI) of 26.8 and a standard deviation of 7.42. Compute a 90% confidence interval for the mean BMI of young women.

26.322 < μ < 27.2779 Explanation: T-Interval in Excel

For a standard Normal distribution, find the approximate proportion of observations less than 1.69. A. 0.0455 B. 0.1455 C. 0.9545 D. 0.9045 E. 1.0045

C. 0.9545 Explanation: see pic

How many hospital-based surgeons are OB/GYNs? A. 32,024 B. 12,225 C. 6,734 D. 24,150 E. None of the above.

C. 6,734 Explanation: Count

A Senator wants to know what the voters of his state think of proposed legislation on gun control. He mails a questionnaire on the subject to an SRS of 2500 voters in his state. His staff reports that 448 questionnaires have been returned, 343 of which support the legislation. This is an example of A. a survey with little bias because it was the voters who elected the senator. B. a survey with little bias because a large SRS was used. C. a survey containing nonresponse. D. all of the above.

C. a survey containing nonresponse. Explanation: Some people who were sent the questionnaire did not respond, leading to non response

A television station is interested in predicting whether or not voters are in favor of an increase in the state sales tax. It asks its viewers to phone in and indicate whether they support or are opposed to an increase in the state sales tax in order to generate additional revenue for education. Of the 2633 viewers who phone in, 1474 (55.98%) are opposed to the increase. The population of interest is A. all regular viewers of the television station who own a phone and have participated in similar phone surveys in the past. B. the 2633 viewers who phoned in. C. all people who will vote on the sales tax increase on the date of the vote. D. the 1474 viewers who were opposed.

C. all people who will vote on the sales tax increase on the date of the vote. Explanation: Population would be everyone who could have possibly participated in the study, not only the people who did

Can pleasant aromas help a student learn better? Two researchers believed that the presence of a floral scent could improve a person's learning ability in certain situations. They had twenty-two people work through a pencil and paper maze six times, three times while wearing a floral-scented mask and three times while wearing an unscented mask. The three trials for each mask closely followed one another. Testers measured the length of time it took the subjects to complete each of the six trials. They reported that, on average, the subjects wearing the floral-scented mask completed the maze more quickly than those wearing the unscented mask, though the difference was not statistically significant. This study is A. an observational study, but not an experiment. B. a convenience sample. C. an experiment, but not a double-blind experiment. D. a double-blind experiment.

C. an experiment, but not a double-blind experiment. Explanation: Things are being changed, making it an experiment, but the testers knew which masks were which

A news release for a diet product company reports: There's good news for the 65 million Americans currently on a diet. Its study showed that people who lose weight can keep it off. The sample was 20 graduates of the company's program who endorse it in commercials. The results of the sample are probably A. biased, understating the effectiveness of the diet. B. unbiased, but they could be more accurate. A larger sample size should be used. C. biased, overstating the effectiveness of the diet. D. None of the above.

C. biased, overstating the effectiveness of the diet. Explanation: Overstated the effectiveness by using a small sample size

An instructor wishes to examine whether a relationship exists between a STAT 200 student's year in school (1, 2, 3, 4, other) and opinion about "clickers" (a student personal response system) being useful to their learning (with responses strongly agree, agree, neutral, disagree & strongly disagree). The instructor needs to construct a A. scatterplot B. stem-and-leaf display C. contingency table D. residual plot E. histogram

C. contingency table Explanation: · Used for non-numerical values

Suppose a straight line is fit to data having response variable yy and explanatory variable xx. Predicting values of yy for values of xx outside the range of the observed data is called A. correlation. B. causation. C. extrapolation. D. contingency. E. None of the above.

C. extrapolation. Explanation: Extrapolation is when we predict values for points outside the range of data taken

In order to assess the opinion of students at the Ohio State University on campus safety, a reporter for the student newspaper interviews 15 students he meets walking on the campus late at night who are willing to give their opinion. The sample obtained is A. a simple random sample of students feeling safe. B. a probability sample of students with night classes. C. probably biased. D. a stratified random sample of students feeling safe.

C. probably biased. Explanation: It is biased because they were chosen in a non-random way

A marketing class designs two videos advertising an expensive Mercedes sports car. They test the videos by asking fellow students to view both (in random order) and say which makes them more likely to buy the car. Mercedes should be reluctant to agree that the video favored in this study will sell more cars because A. this is an observational study, not an experiment. B. the study used matched pairs design instead of a completely randomized design. C. results from students may not generalize to the older and richer customers who might buy a Mercedes. D. None of the above.

C. results from students may not generalize to the older and richer customers who might buy a Mercedes. Explanation:

A student organization wanted to study voting preferences in its student body during the 2012 presidential election. They selected 120 students at random from each class, freshmen through seniors. The sampling technique being used is A. convenience sampling B. a simple random sampling. C. stratified random sampling D. volunteer sampling E. multistage sampling

C. stratified random sampling Explanation: They selected from each class, which is a division of a bigger population. Stratified random sampling involves the division of a population into smaller subgroups

A television station is interested in predicting whether or not voters are in favor of an increase in the state sales tax. It asks its viewers to phone in and indicate whether they support or are opposed to an increase in the state sales tax in order to generate additional revenue for education. Of the 2633 viewers who phone in, 1474 (55.98%) are opposed to the increase. The sample is A. the 1474 viewers were opposed to the increase. B. all people who will vote on the sales tax increase on the data of the vote. C. the 2633 viewers who phoned in. D. all regular viewers of the television station who own a phone and have participated in similar phone surveys in the past.

C. the 2633 viewers who phoned in. Explanation: Sample is all the people in the study

A marketing experiment compares four different types of packaging for blank computer CDs. Each type of packaging can be presented in three different colors. Each combination of package type with a particular color is shown to 40 potential customers, who rate the overall attractiveness on a scale of 1 to 6. The experimental units in this experiment are A. the three different colors. B. the measure of attractiveness C. the potential customers. D. type of packaging and color.

C. the potential customers. Explanation: Experimental units are the people being studied

A researcher measures the correlation between two variables. This correlation tells us A. whether a cause-and-effect relation exists between two variables. B. whether or not a scatterplot shows an interesting pattern. C. the strength of a straight line relation between two variables. D. whether there is a relation between two variables. E. None of the above.

C. the strength of a straight line relation between two variables. Explanation:

A gambler conducts a study to determine whether the time it took a horse to run its last race can be used to predict the time it takes the horse to run its next race. In this study, the explanatory variable is A. all horses used in the study. B. the time it takes a horse to run its next race. C. the time it took a horse to run its last race. D. the gambler's winnings. E. None of the above.

C. the time it took a horse to run its last race. Explanation: Explanatory variable is the independent variable

In order to assess the opinion of students at the Ohio State University on campus safety, a reporter for the student newspaper interviews 15 students he meets walking on the campus late at night who are willing to give their opinion. The method of sampling used is A. a census. B. simple random sampling. C. voluntary response. D. the Gallup Poll.

C. voluntary response. Explanation: The participants were self-chosen by walking up to them, which is voluntary response

A proficiency examination was given to 100 students. The breakdown of the exam results among male and female students is shown in the following table. Which of the following statements is correct about the two variables: gender and exam result (pass or fail)? A. They are independent because there is equal number of males and females among students who passed. B. They are not independent because the percentage of males among students who failed is not the same as the percentage of females among students who failed. C. They are not independent because the number of males among students who passed is not the same as the number of males among students who failed. D. They are not independent because the percentage of males among students who passed is not the same as the percentage of males among students who failed.

D. They are not independent because the percentage of males among students who passed is not the same as the percentage of males among students who failed. Explanation:

One hundred volunteers who suffer from severe depression are available for a study. Fifty are selected at random and are given a new drug that is thought to be particularly effective in treating severe depression. The other fifty are given an existing drug for treating severe depression. A psychiatrist evaluates the symptoms of all volunteers after four weeks in order to determine if there has been substantial improvement in the severity of the depression. (b) Suppose the volunteers were first divided into men and women, and then half of the men were randomly assigned to the new drug and half of the women were assigned to the new drug. The remaining volunteers received the other drug. This would be an example of A. confounding. The effects of gender will be mixed up with the effects of the drugs. B. a matched pairs design. C. replication. D. a block design.

D. a block design. Explanation: The people were divided into gender blocks then treatments are carried out in both blocks

A plot of the residuals will indicate if a line is a good fit to the data if the plot A. shows large residuals in a symmetric pattern. B. shows a curved pattern. C. shows increasing or decreasing spread about a line. D. has no systematic pattern. E. None of the above.

D. has no systematic pattern. Explanation: There should be no patterns in plots of residuals

A phone-in poll conducted by a newspaper reported that 69% of those who called in liked ''real TV''. (a) The unknown true percentage of American citizens who like ''real TV'' is a A. statistic. B. population. C. sample. D. parameter. (b) The number 69% is a A. statistic. B. population. C. parameter. D. sample.

D. parameter. A. statistic.

The mean height of American women is 64.5 inches. Suppose we select ten American women at random and the mean of the heights of the ten women is 61.7 . (a) The number 64.5 is a A. statistic. B. population. C. sample. D. parameter. (b) The number 61.7 is a A. parameter. B. statistic. C. population. D. sample.

D. parameter. B. statistic.

Can one predict a student's score on the midterm exam in a statistics course from the number of hours the student spent studying for the exam? To explore this, the teacher of the course asks students how many hours they spent studying for the exam and then makes a scatterplot of the time students spent studying and their scores on the exam. In making the scatterplot, the teacher should A. use a plotting scale that makes the overall trend roughly linear. B. first determine if the scores on the exam approximately follow a normal distribution. C. plot the score on the exam on the horizontal axis. D. plot time spent studying for the exam on the horizontal axis. E. None of the above.

D. plot time spent studying for the exam on the horizontal axis. Explanation: Independent variable should be on the x-axis

A researcher wishes to determine whether the rate of water flow (in liters per second) over an experimental soil bed can be used to predict the amount of soil washed away (in kilograms). In this study, the explanatory variable is the A. size of the soil bed. B. depth of the soil bed. C. amount of eroded soil. D. rate of water flow. E. None of the above.

D. rate of water flow. Explanation: Explanatory variable is the independent variable

Researchers wish to determine if a new experimental medication will reduce the symptoms of allergy sufferers without the side-effect of drowsiness. To investigate this question, the researchers give the new medication to 50 adult volunteers who suffer from allergies. Forty-four of these volunteers report a significant reduction in their allergy symptoms without any drowsiness. The experimental units are A. the six volunteers who did not report a significant reduction in their allergy symptoms without any drowsiness. B. the researchers. C. the 44 volunteers who reported a significant reduction in their allergy symptoms without any drowsiness. D. the 50 adult volunteers.

D. the 50 adult volunteers. Explanation: People who are being experimented on

A marketing experiment compares four different types of packaging for blank computer CDs. Each type of packaging can be presented in three different colors. Each combination of package type with a particular color is shown to 40 potential customers, who rate the overall attractiveness on a scale of 1 to 6. The factors are A. the rating scale and package combination. B. the three different colors. C. the potential customers. D. type of packaging and color.

D. type of packaging and color. Explanation:

To assess the opinion of students at The Ohio State University about campus safety, a reporter for the student newspaper interviews 15 students she meets walking on the campus late at night who are willing to give their opinion. The method of sampling used is A. a census B. multistage sampling C. a simple random sampling. D. voluntary response E. the Gallup Poll

D. voluntary response Explanation: The participants were self-chosen by walking up to them, which is voluntary response

One hundred volunteers who suffer from severe depression are available for a study. Fifty are selected at random and are given a new drug that is thought to be particularly effective in treating severe depression. The other fifty are given an existing drug for treating severe depression. A psychiatrist evaluates the symptoms of all volunteers after four weeks in order to determine if there has been substantial improvement in the severity of the depression. (c) The factor in this study is A. the use of a psychiatrist to evaluate the severity of depression. B. the extent to which the depression was reduced. C. the use of randomization and the fact that this was a comparative study. D. which treatment the volunteers receive.

D. which treatment the volunteers receive. Explanation: Factor is the type of treatment

Is this data skewed to the right, symmetric, or skewed to the left?

Skewed Right Explanation: The data is skewed right when the tail is to the right

The amounts of 6 restaurant bills and the corresponding amounts of the tips are given in the below. Assume that bill amount is the explanatory variable and tip amount the response variable. According to the regression equation, for every $10 increase in the bill, the tip should ________ by ________

increase, $1.83 Explanation: Found by subtracting two $10 values apart; Put $10 into the equation, then $20 and subtract to find the difference

The sample size needed to estimate the difference between two population proportions to within a margin of error mm with a significance level of αα can be found as follows. In the expression m= z∗ sqrt(p1(1−p1)n1+p2(1−p2)n2 we replace both n1 and n2 by n (assuming that both samples have the same size) and replace each of p1, and p2, by 0.5 (because their values are not known). Then we solve for n, and get n=(z∗)^2/2m^2 Finally, increase the value of n to the next larger integer number. Find the size of each sample needed to estimate the difference between the proportions of boys and girls under 10 years old who are afraid of spiders. Assume that we want a 99% confidence level and that the margin of error is smaller than 0.03. (Round z to the nearest thousandth.)

n = 3687 Explanation: Follow equation given (make sure to only square m, not 2m)

Albert wants to determine a 99 percent confidence interval for the true proportion of times he rolls a 2 (using a fair, 6-sided die). How many rolls must Albert make to get a margin of error less than or equal to 0.05? Use the guessed value p∗=1/6 for the sample proportion.

n = 369 Explanation: o Z* = 2.576 o M = .05 o P = 1/6 o n = (pic)

Beth wants to determine a 90 percent confidence interval for the true proportion of high school students in the area who attend their home basketball games. How large of a sample must she have to get a margin of error less than 0.04? Use the value p∗=1/2 for the sample proportion.

n = 423 Explanation: o Z* = 1.645 o M = .04 o P = ½ o n = (pic)

Find the linear correlation coefficient rr to determine whether there is a correlation between the two variables. (Note: Use your calculator. You may want to create a scatterplot as a reality check.) (0.8, 0.8)(1.4, 1.4) (2.2, 2.2) (3.1, 3.1) (4.4, 4.4) (5, 5) (6, 6) (7.5, 7.5) (8.1, 8.1) (9.6, 9.6) (10.1, 10.1) (11, 11) (12.5, 12.5) (13.7, 13.7) (14.1, 14.1)

r = 1 Explanation: Find the r value using the calculator (input values, STAT, CALC, 8). It is perfect because it is 1

4.27 minutes Explanation: Find the equation in the calculator, then plug the 171 cm into the equation; 2.15 + 0.0053(400)

76.331 + .099x Explanation:

According to CBS News, 48% of Americans believe in ghosts. For the problems below, assume that is the actual population percentage. Suppose we choose a simple random sample of 68 Americans. For each problem, select the best response: (a) The probability of obtaining a sample proportion of 0.5 or higher is approximately A. 0.3707 B. 0.31465 C. 0.68535 D. 0.6293 (b) Suppose we wanted the standard deviation of the sample proportion to be half of what it is for a sample of size 68. To achieve this, we should take a sample of size A. 17 B. 34 C. 136 D. 272 (c) The sampling distribution of the proportion of those in the sample who believe in ghosts is approximately A. N(0.48, 0.0606) B. N(0.48, 0.0037) C. N(0.048,0.0037) D. N(0.048, 0.0606)

A. 0.3707 D. 272 A. N(0.48, 0.0606)

How many general surgeons are hospital based? A. 12,225 B. 38,011 C. 25,901 D. 24,128 E. None of the above.

A. 12,225 Explanation: Count

How many surgeons are ophthalmologists? A. 15,540 B. 73,970 C. 12,328 D. 18,026 E. None of the above.

A. 15,540 Explanation: Count

About what percent of men are between 69 and 74 inches? A. 47.5%. B. 5%. C. 16%. D. 95%. E. None of the above.

A. 47.5%. Explanation: From mean to 2 standard deviations out, the empirical rule states the percentage would be 47.5%

Archaeologists plan to examine a sample of 5-meter-square plots near an ancient Greek city for artifacts visible in the ground. They choose separate samples of plots from floodplain, coast, foothills, and high hills. What kind of sample is this? A. A stratified random sample. B. A voluntary response sample. C. A simple random sample. D. None of the above.

A. A stratified random sample. Explanation: They were broken up into smaller groups from the population then sampled

Refer to the following scenario. An epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the area. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 331 people living in East Vancouver and finds that 30 have recently had the flu. For each of the following statements, specify whether the statement is a correct interpretation of the 95% confidence interval for the true proportion of East Vancouver residents who have recently had the flu. A. 9.06% (30/331) of East Vancouver residents have recently had the flu. B. There is a 95% probability that the true proportion of East Vancouver residents who have recently had the flu equals 30/331. C. If another random sample of 331 East Vancouver residents is drawn, there is a 95% probability that the sample proportion of East Vancouver residents who have recently had the flu equals 30/331. D. If many random samples of 331 East Vancouver residents are drawn, 95% of the resulting confidence intervals will contain the value of the true proportion of East Vancouver residents who have recently had the flu. E. If many random samples of 331 East Vancouver residents are drawn, 95% of the resulting confidence intervals will contain the value 30/331.

A. False B. False C. False D. True E. False

A small college has 500 male and 600 female undergraduates. A simple random sample of 50 of the male undergraduates is selected, and, separately, a simple random sample of 60 of the female undergraduates is selected. The two samples are combined to give an overall sample of 110 students. The overall sample is A. a stratified random sample. B. a multistage sample. C. a systematic sample. D. convenience sampling. E. a simple random sample.

A. a stratified random sample. Explanation: The population was broken up into groups of males and females, a division of the bigger population of undergraduate students

One hundred volunteers who suffer from severe depression are available for a study. Fifty are selected at random and are given a new drug that is thought to be particularly effective in treating severe depression. The other fifty are given an existing drug for treating severe depression. A psychiatrist evaluates the symptoms of all volunteers after four weeks in order to determine if there has been substantial improvement in the severity of the depression. The study would be double-blind if A. neither the volunteers nor the psychiatrist knew which treatment any person had received. B. all volunteers were not allowed to see the psychiatrist nor the psychiatrist allowed to see the volunteers during the session in which the psychiatrist evaluated the severity of the depression. C. neither drug had any identifying marks on it. D. None of the above.

A. neither the volunteers nor the psychiatrist knew which treatment any person had received. Explanation: Double blind is neither party knows the treatment

Considering the data value 8 and using the 1.5 x IQR rule, we would A. not classify the value 8 as an outlier because it is not more that 1.5 x IQR below the first quartile B. classify the value 8 as an outlier because it is more that 1.5 x IQR below the median C. Classify the value 8 as an outlier because it is more that 1.5 x IQR below the first quartile D. not classify the value 8 as an outlier because it is not more that 1.5 x IQR below the median

A. not classify the value 8 as an outlier because it is not more that 1.5 x IQR below the first quartile Explanation: IQR is the difference between q1 and q3. Multiplying this data by +- 1.5 would show that 8 is within this range and therefore is not an outlier

An opinion poll contacts 1849 adults and asks them, " Which political party do you think has better ideas for leading the country in the 21st century?" In all, 516 of the 1849 say, " The Democrats." The sample in this setting is A. the 1849 people interviewed. B. the 516 people who chose the Democrats. C. all 235 million adults in the United States. D. None of the above.

A. the 1849 people interviewed. Explanation: Sample is people who participated in the study

A marketing research firm wishes to determine if the residents of Caldwell, Idaho, would be interested in a new downtown restaurant. The firm selects a simple random sample of 165 phone numbers from the Caldwell phone book and calls each household. Only 32 of those called are willing to participate in the survey, and 16 participants would support a new downtown restaurant. The sample in this survey is A. the 32 households that participated in the study. B. all households in the Caldwell phone book. C. the 165 phone numbers chosen. D. all residents of Caldwell. E. None of the above.

A. the 32 households that participated in the study. Explanation: Sample is the people who participated in the study

For the following problems, select the best response: (a) The sampling distribution of a statistic is A. the distribution of values taken by a statistic in all possible samples of the same size from the same population. B. the mechanism that determines whether or not randomization was effective. C. the probability that we obtain the statistic in repeated random samples. D. the extent to which the sample results differ systematically from the truth. (b) Sampling variation is caused by A. changes in a population parameter that cannot be predicted. B. systematic errors in our procedure. C. changes in a population parameter from sample to sample. D. random selection of a sample. (c) A statistic is said to be unbiased if A. the mean of its sampling distribution is equal to the true value of the parameter being estimated. B. it is used for only honest purposes. C. the survey used to obtain the statistic was designed so as to avoid even the hint of racial or sexual prejudice. D. both the person who calculated the statistic and the subjects whose responses make up the statistic were truthful.

A. the distribution of values taken by a statistic in all possible samples of the same size from the same population. D. random selection of a sample. A. the mean of its sampling distribution is equal to the true value of the parameter being estimated.

A marketing research firm wishes to determine if the residents of Caldwell, Idaho, would be interested in a new downtown restaurant. The firm selects a simple random sample of 165 phone numbers from the Caldwell phone book and calls each household. Only 32 of those called are willing to participate in the survey, and 16 participants would support a new downtown restaurant. The chance that all 165 phone numbers chosen are located in one particular neighborhood in Caldwell is A. the same as for any other set of 165 phone numbers. B. 165 divided by the size of the population of Caldwell. C. exactly 0. Simple random sampling will spread out the locations of the phone numbers selected. D. reasonably large due to the ''cluster'' effect. E. None of the above.

A. the same as for any other set of 165 phone numbers.

A study of human development showed two types of movies to a group of children. Crackers were available in a bowl, and the investigators compared the number of crackers eaten by the children while watching the different kinds of movies. One kind was shown at 8 A.M. and another at 11 A.M. It was found that during the movie shown at 11 A.M., more crackers were eaten than during the movie shown at 8 A.M. The investigators concluded that the different types of movies had an effect on appetite. A lurking variable in this experiment is A. the time the movie was shown. B. the different kinds of movies. C. the bowls. D. the number of crackers eaten.

A. the time the movie was shown. Explanation: The times can cause the children to be hungry instead of the movie itself

For a Normal distribution with mean 1.4 and standard deviation 0.6, 23 percent of the observations are greater than what value? A. 1.6603 B. 1.8433 C. 1.7933 D. 0.92165 E. -1.9433

B. 1.8433 Explanation: see pic

How many different conditional distributions could be constructed from these data? A. 4 B. 7 C. 2 D. 3 E. None of the above.

B. 7 Explanation: Number of variables (surgeon a, surgeon b, place a, place b, etc.); Conditional distribution is the number of different variables (office, hospital, other, general surgery, OBGYN, etc.)

A fast-food restaurant chain looks at average sales for its rural and suburban stores. Sales at mall-based locations are generally higher than sales at stand-alone locations. There are few mall-based locations among rural stores, but many mall-based locations among suburban stores. The company finds that rural stores at mall-based locations have higher sales than suburban stores at mall-based locations. Rural stores in stand-alone locations also have higher sales than suburban stores in stand-alone locations. Yet suburban stores as a group have higher sales than rural stores. This finding is A. due to comparing two conditional distributions that should not be compared. B. an example of Simpsons paradox: rural stores do better in both types of locations but worse overall because they have more stand-alone locations. C. the result of comparing two marginal distributions. D. not possible: if both mall-based and stand-alone locations that are rural have higher sales than those that are suburban, then all rural stores together must have higher sales than all suburban stores together. E. None of the above.

B. an example of Simpsons paradox: rural stores do better in both types of locations but worse overall because they have more stand-alone locations. Explanation: Simpson's paradox is when a trend appears in several different groups of data but disappears or reverses when these groups are combined.

A study of the effects of running on personality involved 231 male runners who each ran about 20 miles a week. The runners were given the Cattell Sixteen Personality Factors Questionnaire, a 187-item multiple-choice test often used by psychologists. A news report (The New York Times, Feb. 15, 1988) stated, The researchers found statistically significant personality differences between the runners and the 30-year-old male population as a whole. A headline on the article said, Research has shown that running can alter one's moods. This study was A. a randomized, double-blind experiment. B. an observational study, but not an experiment. C. an experiment, but not a double-blind experiment. D. a double-blind experiment, but not a randomized experiment.

B. an observational study, but not an experiment. Explanation: Nothing was directly manipulated, making it observational

The Nurses' Health Study has interviewed a sample of more than 100,000 female registered nurses every two years since 1976. The study finds that " light-to-moderate drinkers had a significantly lower risk of death" than either nondrinkers or heavy drinkers. The Nursers' Health Study is A. an experiment. B. an observational study. C. Can't tell without more information.

B. an observational study. Explanation: Interview makes it observational

A study of human development showed two types of movies to a group of children. Crackers were available in a bowl, and the investigators compared the number of crackers eaten by the children while watching the different kinds of movies. One kind was shown at 8 A.M. and another at 11 A.M. It was found that during the movie shown at 11 A.M., more crackers were eaten than during the movie shown at 8 A.M. The investigators concluded that the different types of movies had an effect on appetite. This is an example of a A. simple random sample. B. matched pairs design. C. block design. D. None of the above.

B. matched pairs design. Explanation: It is random block design that has only 2 treatment conditions and subjects can be grouped into pairs based on a blocking variable

A television station is interested in predicting whether or not voters are in favor of an increase in the state sales tax. It asks its viewers to phone in and indicate whether they support or are opposed to an increase in the state sales tax in order to generate additional revenue for education. Of the 2633 viewers who phone in, 1474 (55.98%) are opposed to the increase. In this case, the sample obtained is A. a simple random sample. B. probably biased. C. a probability sample in which each person in the population has the same chance of being in the sample. D. a stratified random sample.

B. probably biased. Explanation: They are probably biased because the sample is only people calling into the show and would not have the chance to include people who do not call in

In order to assess the opinion of students at the Ohio State University on campus safety, a reporter for the student newspaper interviews 15 students he meets walking on the campus late at night who are willing to give their opinion. ]The sample is A. all those students walking on campus late at night. B. the 15 students interviewed. C. all students approached by the reporter. D. all students at universities with safety issues.

B. the 15 students interviewed. Explanation: Sample is the people who were studied

The Columbus Zoo conducts a study to determine whether a household's income can be used to predict the amount of money the household will give to the zoo's annual fund drive. The response variable in this study is A. a household's income. B. the amount of money a household gives to the zoo's annual fund drive. C. the Columbus Zoo. D. all households in Columbus. E. None of the above.

B. the amount of money a household gives to the zoo's annual fund drive. Explanation: Response variable is the dependent variable

To completely specify the shape of a Normal distribution, you must give A. the five-number summary. B. the mean and the standard deviation. C. the mean and the median. D. the median and the standard deviation. E. All of the above.

B. the mean and the standard deviation. Explanation: The mean and distribution are the only things needed to use in the empirical rule to find the shape of a normal distribution

A study of human development showed two types of movies to a group of children. Crackers were available in a bowl, and the investigators compared the number of crackers eaten by the children while watching the different kinds of movies. One kind was shown at 8 A.M. and another at 11 A.M. It was found that during the movie shown at 11 A.M., more crackers were eaten than during the movie shown at 8 A.M. The investigators concluded that the different types of movies had an effect on appetite. The response variable in this experiment is A. the different kinds of movies. B. the number of crackers eaten. C. the time the movie was shown. D. the bowls.

B. the number of crackers eaten. Explanation: Response variable is what changes (dependent variable)

A study found a correlation of r = -0.61 between the gender of a worker and his or her income. You may correctly conclude A. women earn more than men on average. B. this is incorrect because r makes no sense here. C. women earn less than men on average. D. an arithmetic mistake was made. Correlation must be positive. E. None of the above.

B. this is incorrect because r makes no sense here

B. visits of the college students. Explanation: Lurking variable is something else that could be causing the results, in this case the visits themselves

Andrew thinks that people living in a rural environment have a healthier lifestyle than other people. He believes the average lifespan in the USA is 77 years. A random sample of 13 obituaries from newspapers from rural towns in Idaho gives x¯=79.16 and s=0.62. Does this sample provide evidence that people living in rural Idaho communities live longer than 77 years? (a) State the null and alternative hypotheses: (b) Find the test statistic, t= (c) Does this sample provide evidence that people living in rural Idaho communities live longer than 77 years? (Use a 10% level of significance)

(a) H0: mu = 77 Ha: mu > 77 (b) 12.5612 (c) Yes Explanation: T-test in Excel

Given the following data set, let x be the explanatory variable and y be the response variable. If a least-squares line was fitted to this data, what percentage of the variation in the y would be explained by the regression line? (Enter your answer as a percent.)

90.3% Explanation: r2

For a standard Normal distribution, find the approximate proportion of observations between -0.04 and 0.37. A. 0.1603 B. 0.2103 C. 0.1103 D. 0.9397 E. 0.8397

A. 0.1603 Explanation: see pic

A committee on community relations in a college town plans to survey local businesses about the importance of students as customers. From telephone book listings, the committee chooses 175 businesses at random. Of these, 71 return the questionnaire mailed by the committee. The population for this study is A. all businesses in the college town. B. the 175 businesses chosen. C. the 71 businesses that returned the questionnaire. D. None of the above.

A. all businesses in the college town. Explanation: Population is all businesses who could have been chosen

A. herbal tea. Explanation: Explanatory variable is what is causing the outcome

Match the following sample correlation coefficients with the explanation of what that correlation coefficient means. Type the correct letter in each box. _____ r=−.97 ______ r=1 ______ r=.92 ______ r=−1 A. a perfect negative relationship between x and y B. a perfect positive relationship between x and y C. a strong negative relationship between x and y D. a strong positive relationship between x and y

___C___ r=−.97 ___B___ r=1 ___D___ r=.92 ___A___ r=−1 Explanation: Perfect relationships are equal to 1

Match the correlation coefficients with their scatterplots. Select the letter of the scatterplot below which corresponds to the correlation coefficient. (Click on image for a larger view.) ______ r=0.89 ______ r=−0.49 ______ r=−0.97 ______ r=0.22

___D___ r=0.89 ___B___ r=−0.49 ___C___ r=−0.97 ___A___ r=0.22 Explanation: The steeper the line, the closer the r value is to 1

What is the value of t∗, the critical value of the tt distribution for a sample of size 18, such that the probability of being greater than t∗ is 11%? t* =

t* = 2.5669 Explanation: see pic

Physicians at a clinic gave what they thought were drugs to 920 patients. Although the doctors later learned that the drugs were really placebos, 57 % of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patient's condition improving is 0.56. Test the hypotheses that the proportion of patients improving is >0.56. Find the test statistic: Find the P-value:

z= .611 P= .27 Explanation: 1-PropZTest on calc. o N= 920 o X= 57% of 920 o Po= .56 o >

A survey of 1465 people who took trips revealed that 139 of them included a visit to a theme park. Based on those survey results, a management consultant claims that less than 10% of trips include a theme park visit. Test this claim using the α=0.05 significance level. (a) What is the test statistic (b) What is the P-value (c) The conclusion is A. There is not sufficient evidence to support the claim that less than 10 % of trips include a theme park visit. B. There is sufficient evidence to support the claim that less than 10 % of trips include a theme park visit.

(a) -.653 (b) .256 (c) A. There is not sufficient evidence to support the claim that less than 10 % of trips include a theme park visit. Explanation: 1-PropZTest calc o N= 1465 o X= 139 o Po= .1 o <

An article in the Washington Post on March 16, 1993 stated that nearly 45 percent of all Americans have brown eyes. A random sample of n=76 Americans found 28 with brown eyes. We test: H0:p=.45 Ha:p≠.45 (a) What is the z-statistic for this test? (b) What is the P-value of the test?

(a) -1.43 (b) .152 Explanation: 1-PropZTest calc. o N= 76 o X= 28 o Po=.45 o Not =

Given the following data set, let x be the explanatory variable and y be the response variable. Compute the correlation coefficient: r=_______

-.95 Explanation: Calculator

Our bodies have a natural electrical field that is known to help wounds heal. Does changing the field strength slow healing? A series of experiments with newts investigated this question. In one experiment, the two hind limbs of twelve newts were assigned at random to either experimental or control groups. This is a matched pairs design. The electrical field in the experimental limbs was reduced to zero by applying a voltage. The control limbs were left alone. The table shows the rates at which new cells closed a razor cut in each limb, in micrometers per hour. Compute a 90% confidence interval for the difference in rates (Control −− Experimental). Newt: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, Control: 36, 41, 39, 42, 44, 39, 39, 56, 33, 20, 49, 30 Experimental: 28, 31, 27, 33, 33, 38, 45, 25, 28, 33, 47, 23

.866 < μd < 11.967 Explanation: Find difference of table values, then put into excel T-Interval

.985 Explanation: Calculator

A simple random sample of size 18 is drawn from a population that has a normal distribution. The sample has a mean of 113.5 and a standard deviation of 4.5. Give the standard error of the mean:

1.0606 Explanation: T-Interval test in excel

What is the mean lean body mass of the obese monkeys? Include at least three decimal places of accuracy.

10.867 kilograms Explanation: · mean of chunky monkeys

A random sample of 1400 home owners in a particular city found 294 home owners who had a swimming pool in their backyard. Find a 95% confidence interval for the true percent of home owners in this city who have a swimming pool in their backyard. Express your results to the nearest hundredth of a percent.

18.945 to 23.219 % Explanation: 1-PropZInt Excel

A marketing experiment compares five different types of packaging for blank computer CDs. Each type of packaging can be presented in four different colors. Each combination of package type with a particular color is shown to 40 potential customers, who rate the overall attractiveness on a scale of 1 to 5. How many treatments are there?

20 Explanation: 4 colors x 5 packaging types = 20 treatments

One statistic used to assess professional golfers is driving accuracy, the percent of drives that land in the fairway. In 2012, driving accuracy for PGA Tour professionals ranged from about 45% to about 75%. Rory McIlroy, the highest winner on the PGA tour in 2012, only hits the fairway about 57% of the time. McIlroy is also one of the longest drivers on the tour, and increased distance is generally associated with decreased accuracy. Assuming that a binomial distribution can be used, what is the expected number of fairways that McIlroy hits in a round in which he hits 12 drives?

6.84 Explanation: Np = 12 x .57

Animals and people that take in more energy than they expend will get fatter. Here are data on 12 rhesus monkeys: 6 lean monkeys (4% to 9% body fat) and 6 obese monkeys (13% to 14% body fat). The data report the energy expended in 24 hours (kilojoules per minute) and the lean body mass (kilograms, leaving out fat) for each monkey. What is the mean lean body mass of the lean monkeys? Include at least three decimal places of accuracy.

8.750 kilograms Explanation: mean of lean monkeys

A recent survey showed that among 650 randomly selected subjects who completed 4 years of college, 142 smoke and 508 do not smoke. Determine a 95% confidence interval for the true proportion of the given population that smokes.

95% CI: .1883 to .2520 Explanation: 1-PropZInt in Excel

A plausible value for the correlation between weight and mpg is A. -0.9 B. +0.7 C. +0.2 D. -1.0

A. -0.9 Explanation: It is a steep, negative line

The proportion of observations from standard Normal distribution that takes values less than z = 1.15 is about A. 0.8749 B. 0.1251 C. 0.8531 D. 0.2436 E. None of the above.

A. 0.8749 Explanation: see pic

A Senator wants to know what the voters of his state think of proposed legislation on gun control. He mails a questionnaire on the subject to an SRS of 2500 voters in his state. His staff reports that 448 questionnaires have been returned, 343 of which support the legislation. The population is A. the voters in his state. B. the 2500 voters receiving the questionnaire. C. the 448 letters received. D. the 343 letters supporting the legislation.

A. the voters in his state. Explanation: Population is all people who could have been chosen for a study

For a Normal distribution with mean 200 and standard deviation 15, 35 percent of the observations are less than what value? A. 213.64 B. 194.22 C. 233.06 D. 174.8 E. 155.38

B. 194.22 Explanation: see pic

a) How many different marginal distributions could be constructed from these data? A. 7 B. 2 C. 4 D. 3 E. None of the above.

B. 2 Explanation: Marginal distributions are the # of types of variables (in this case, the place and the type of surgery)

The scores of adults on an IQ test are approximately Normal with mean 100 and standard deviation 15. Corinne has 118 on such test. She scores higher than what percent of all adults? A. About 12%. B. About 88%. C. About 50%. D. About 98%. E. None of the above.

B. About 88%. Explanation: This is value is between 1 and 2 standard deviations out, so it's about 88%

Which of these variables is least likely to have a Normal distribution? A. Heights of 100 white pine trees in a forest. B. Income per person for 150 different countries. C. Lengths of 50 newly hatched pythons. D. None of the above.

B. Income per person for 150 different countries. Explanation: Most countries have around the same income level

There is A. a positive correlation between x and y B. a perfect positive correlation between x and y C. a perfect negative correlation between x and y D. a negative correlation between x and y E. a nonlinear correlation between x and y F. no correlation between x and y

B. a perfect positive correlation between x and y Explanation:

A lurking variable is A. and variable that produces a large residual. B. a variable that is not among the variables studied but that affects the response variable. C. the true cause of a response. D. the true variable that is explained by the explanatory variable. E. None of the above.

B. a variable that is not among the variables studied but that affects the response variable. Explanation: Affect response variable but is not part of the study

A Senator wants to know what the voters of his state think of proposed legislation on gun control. He mails a questionnaire on the subject to an SRS of 2500 voters in his state. His staff reports that 448 questionnaires have been returned, 343 of which support the legislation. The sample is: A. the 2500 voters receiving the questionnaire B. the 448 letters received. C. the 343 letters supporting the legislation. D. the voters in his state.

B. the 448 letters received. Explanation: The letters that were used for study are the sample

The proportion of observations from standard Normal distribution that take values larger than z = -0.75 is about A. 0.2266 B. 0.3789 C. 0.7734 D. 0.8023 E. None of the above.

C. 0.7734 Explanation: see pic

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. About 95% of all pregnancies last between A. 218 and 314 days. B. 260 and 320 days. C. 234 and 298 days. D. 250 and 282 days. E. None of the above.

C. 234 and 298 days. Explanation: Using the empirical rule and looking 2 standard deviations out, you can find where 95% of pregnancies lie

The scatterplot suggests A. there is a positive association between height and volume. B. there is an outlier in the plot. C. both A and B. D. neither A nor B.

C. both A and B.

In this study, the response variable is A. height or volume. It doesn't matter which is considered the response. B. neither height nor volume. The measuring instrument used to measure height is the response variable. C. volume. D. height.

C. volume. Explanation: Response variable is on the y axis

For each problem, select the best response. (a) A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS of 1200 registered voters and found that 620 would vote for the Republican candidate. Let p represent the proportion of registered voters in the state who would vote for the Republican candidate. A 90 percent confidence interval for p is: A. 0.517 ± 0.249 B. 0.517 ± 0.028 C. 0.517 ± 0.014 D. 0.517 ± 0.024 (b) A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think the drinking age should be lowered to 18. He asks, 'Do you think the drinking age should be reduced to 18 in light of the fact that 18 year olds are eligible for military service?' He asks listeners to phone in and vote 'yes' if they agree the drinking age should be lowered to 18, and 'no' if not. Of the 100 people who phoned in, 70 answered 'yes.' Which of the following assumptions for inference about a proportion using a confidence interval are violated? A. The sample size is large enough so that the count of failures n(1−p^) is 15 or more. B. The sample size is large enough so that the count of successes np̂ is 15 or more. C. The population is at least ten times as large as the sample. D. The data are an SRS from the population of interest. (c) A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS of 1200 registered voters and found that 620 would vote for the Republican candidate. Let p represent the proportion of registered voters in the state who would vote for the Republican candidate. How large a sample n would you need to estimate p with a margin of error 0.01 with 95 percent confidence? Use the guess p=.5 as the value of p. A. 49 B. 1500 C. 9604 D. 4800

D. 0.517 ± 0.024 D. The data are an SRS from the population of interest. C. 9604

About what percent of men are taller than 69 inches? A. 32%. B. 16%. C. 68%. D. 50%. E. None of the above.

D. 50%. Explanation: Since it's the mean, 50% would be taller

Simple random sampling A. guarantees valid results. B. reduces bias resulting from poorly worded questions. C. reduces bias resulting from the behavior of the interviewer. D. offsets bias resulting from undercoverage and nonresponse. E. None of the above.

E. None of the above.

Researchers wish to determine if a new experimental medication will reduce the symptoms of allergy sufferers without the side-effect of drowsiness. To investigate this question, the researchers give the new medication to 50 adult volunteers who suffer from allergies. Forty-four of these volunteers report a significant reduction in their allergy symptoms without any drowsiness. This is an example of A. a double blind experiment. B. the establishing of a causal relationship. C. a randomized study. D. a block design. E. None of the above.

E. None of the above. Explanation:

A marketing research firm wishes to determine if the residents of Caldwell, Idaho, would be interested in a new downtown restaurant. The firm selects a simple random sample of 165 phone numbers from the Caldwell phone book and calls each household. Only 32 of those called are willing to participate in the survey, and 16 participants would support a new downtown restaurant. The population of interest is A. all residents of Caldwell. B. the 165 phone numbers chosen. C. the 32 households that participated in the study. D. all households in the Caldwell phone book. E. None of the above.

E. None of the above. Explanation: Population is all people who could have been chosen

Which is bigger for this data set, the mean or the median, or are they about equal?

Mean Explanation: In skewed right data, the mean is always the largest

Calculate the mean and median of the following data: 30, 17, 12, 40, 13, 41, 33, 2430, 17, 12, 40, 13, 41, 33, 24 Include at least three decimal places of accuracy.

Mean: 26.250 Median: 27 Explanation: Mean and Median

A boxplot for a set of data is given below. Find the five-number summary

Minimum: 2 Q1: 3 Median: 6 Q3: 14 Maximum: 16 Explanation: Whiskers are min/max, box outlines are q1/q3, median is middle line

Find the five-number summary for the following 10 values: 38, 38, 34, 30, 27, 25, 23, 34, 8, 37

Minimum: 8 Q1: 25 Median: 32 Q3: 37 Maximum: 38 Explanation: To find q1 and q3, you find the median then find the medians of the two halves

Given the data set below, calculate the range, mean, variance, and standard deviation. Include at least three decimal places of accuracy. 24, 15, 35, 34, 6, 11, 18, 8, 42

Range: 36 Mean: 21.444 Variance: 169.028 Standard Deviation: 13.001 Explanation: Put the data into the calculator or a standard deviation calculator online

An article in the Washington Post on March 16, 1993 stated that nearly 45 percent of all Americans have brown eyes. A random sample of n=55 Americans found 22 with brown eyes. Give the numerical value of the "plus 4" statistic p̃ that is an estimate for p..

p̃ = .4067 Explanation: o N = 55 +4 o X = 22 + 2 o 1-PropZInt (STAT, Test, A)

If X is a binomial random variable with n and p as indicated, compute P(X=k)P(X=k) for each of the following cases: (a) n=3, k=1, p=0.9 P(X=k)= (b) n=4, k=3, p=0.1 P(X=k)= (c) n=4, k=0, p=0.9 P(X=k)= (d) n=6, k=3, p=0.8 P(X=k)=

(a) .027 (b) .0036 (c) .0001 (d) .08192 Explanation: (a) binomialpdf (3, .9, 1) (b) binomialpdf (4, .1, 3) (c) binomialpdf (4, .9, 0) (d) binomialpdf (6, .8, 3)

Researchers wish to determine if a new experimental medication will reduce the symptoms of allergy sufferers without the side-effect of drowsiness. To investigate this question, the researchers give the new medication to 50 adult volunteers who suffer from allergies. Forty-four of these volunteers report a significant reduction in their allergy symptoms without any drowsiness. This study could be improved by A. repeating the study with only the 44 volunteers who reported a significant reduction in their allergy symptoms without any drowsiness, and giving them a higher dosage this time. B. using a control group. C. including people who do not suffer from allergies in the study in order to represent a more diverse population. D. all of the above.

B. using a control group. Explanation:

A proficiency examination was given to 100 students. The breakdown of the exam results among male and female students is shown in the following table. Which of choices (A-D) below gives the conditional distribution of gender for students who failed the exam? A Male 30 (54.5%) Female 25 (45.5%) Total 55 (100%) B Male 55 (55%) Female 45 (45%) Total 100 (100%) C Male 25 (62.5%) Female 15 (37.5%) Total 40 (100%) D Male 25 (25%) Female 15 (15%) Total 100 (100%)

C Male 25 (62.5%) Female 15 (37.5%) Total 40 (100%) Explanation: Look at people who failed

A group of college students believes that herbal tea has remarkable restorative powers. To test their theory, they make weekly visits to a local nursing home, visiting with residents, talking with them, and serving them herbal tea. After several months, many of the residents are more cheerful and healthy. Which of the following may be correctly concluded from this study? A. Herbal tea does improve one's emotional state, at least for the residents of nursing homes. B. There is some evidence that herbal tea may improve one's emotional state. The results would be completely convincing if a scientist had conducted the study rather than a group of college students. C. The results of the study are not convincing because only a local nursing home was used and only for a few months. D. The results of the study are not convincing because the effect of herbal tea is confounded with several other factors.

D. The results of the study are not convincing because the effect of herbal tea is confounded with several other factors. Explanation: Other variables are present that can skew the results

The director of an alumni association for a university wants to look at the relationship between the number of years since graduation and the amount of monetary contribution an alumnus makes to the university. He collects data on 50 alumni who have made contributions this year and fits a least squares regression line to the data, with the monetary contribution as the response variable.James, one of the 50 alumni, has made a contribution which gives a negative residual. Which of the following statements must be true about James' actual contribution? a) It is less than the contribution predicted by the regression line. b) It is less than the average contribution made by the 50 alumni. c) Both (a) and (b). d) Neither (a) nor (b).

a) It is less than the contribution predicted by the regression line. Explanation: Less than predicted but not exactly less than average

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