AP Statistics Exam Review Questions Multiple-Choice

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The figure shows a cumulative relative frequency histogram of 40 scores on a test given in an AP Statistics class. Which of the following conclusions can be made from the graph? (A) There is greater variability in the lower 20 test scores than in the higher 20 test scores. (B) The median test score is less than 50. (C) Sixty percent of the students had test scores above 80. (D) If the passing score is 70, most students did not pass the test. (E) The horizontal nature of the graph for the test scores of 60 and below indicates that those scores occurred most frequently.

(A) There is greater variability in the lower 20 test scores than in the higher 20 test scores.

The graphs of the sampling distributions, I and II, of the sample mean of the same random variable for samples of two different sizes are shown above. Which of the following statements must be true about the sample sizes? (A) The sample size of I is less than the sample size of II. (B) The sample size of I is greater than the sample size of II. (C) The sample size of I is equal to the sample size of II. (D) The sample size does not affect the sampling distribution. (E) The sample sizes cannot be compared based on these graphs.

(B) The sample size of I is greater than the sample size of II.

Lauren is enrolled in a very large college calculus class. On the first exam, the class mean was 75 and the standard deviation was 10. On the second exam, the class mean was 70 and the standard deviation was 15.Lauren scored 85 on both exams. Assuming the scores on each exam were approximately normally distributed, on which exam did Lauren score better relative to the rest of the class? (A) She scored much better on the first exam. (B) She scored much better on the second exam. (C) She scored about equally well on both exams. (D) It is impossible to tell because the class size is not given. (E) It is impossible to tell because the correlation between the two sets of exam scores is not given.

A random sample of 25 households from the Mountainview School District was surveyed. In this survey, data were collected on the age of the youngest child living in each household. The histogram below displays the data collected in the survey. In which of the following intervals is the median of these data located? (A) 0 years old to less than 2 years old (B) 4 years old to less than 6 years old (C) 6 years old to less than 8 years old (D) 8 years old to less than 10 years old (E) 10 years old to less than 12 years old

(D) 8 years old to less than 10 years old

Janelle collected data on the amount of time in minutes each person in a large sample of customers spent in a local store. The data also included recording the gender of each customer. These data were used to generate the boxplots shown below. (A) The range in the amount of time in minutes males in the sample of customers spent in the store is approximately 40 minutes. (B) The mean amount of time in minutes males in the sample of customers spent in the store is approximately 20 minutes. (C) The third quartile of the amount of time in minutes males in the sample of customers spent in the store is approximately 45 minutes. (D) The interquartile range of the amount of time in minutes females in the sample of customers spent in the store is 15 minutes. (E) Approximately half of the males in the sample of customers spent at least as much time in the store as any female in the sample of customers.

(E) Approximately half of the males in the sample of customers spent at least as much time in the store as any female in the sample of customers.

A researcher planning a survey of heads of households in a particular state has census lists for each of the 23 counties in that state. The procedure will be to obtain a random sample of 10 heads of households from each of the 23 counties. Which of the following is a true statement about the resulting sample? I. This is not a proper study because children were not included. II. This stratified random sample is a type of simple random sample because subjects were randomly selected from each county. III. This is not a simple random sample because all possible groups of 230 subjects did not have the same probability of being selected. IV. This study may give important information about the similarities and differences of the 23 counties. A) III and IV B) I and II C) I and III D) I,II, and III E) None of these

A) III and IV

What type of inference? Is there a correlation between test anxiety and exam score performance? Data on x = score on a measure of test anxiety and y = exam score consistent with summary quantities given in the paper "Effects of Humor on Test Anxiety and Performance" (psych. Reports (1999): 1203-1212 appears below. Test to see if the linear regression equation is useful in predicting test score using anxiety score. x 23 14 14 0 7 20 20 20 15 21 y 43 59 48 77 50 52 46 51 51 A)chi-squared Test of Independence B) 2-proportion z-test C) 2-sample t-test D) T-Test for Slope

D) T-Test for Slope

Write Ho and Ha CHECK ALL THAT APPLY Ho: The distributions of proportions of color preferences are the same for truck drivers and sports car drivers. Ha: The distributions of proportions of color preferences are different for truck drivers and sports car drivers. Ho: There is NO association between truck drivers and sports car drivers. Ha: There IS an association between truck drivers and sports car drivers.

Ho: The distributions of proportions of color preferences are the same for truck drivers and sports car drivers. Ha: The distributions of proportions of color preferences are different for truck drivers and sports car drivers.

CONCLUSION. Check all that apply. Assume alpha = 0.05. Since our p-value is less than alpha... Since our p-value is greater than alpha... we REJECT Ho. we FAIL TO REJECT Ho. We HAVE evidence of a greater MEAN amount of active ingredient in the name-brand than the generic-brand. We LACK evidence of a greater MEAN amount of active ingredient in the name-brand than the generic-brand.

Since our p-value is less than alpha... we REJECT Ho. We HAVE evidence of a greater MEAN amount of active ingredient in the name-brand than the generic-brand.

#3 - CONCLUSION. Check all that apply. Since our p-value is less than alpha... Since our p-value is greater than alpha... we REJECT Ho. we FAIL TO REJECT Ho. We HAVE evidence of an association between age-group and whether a U.S. adult consumes 5 or more servings of fruits and veggies per day. We LACK evidence of an association between age-group and whether a U.S. adult consumes 5 or more servings of fruits and veggies per day.

Since our p-value is less than alpha... we REJECT Ho. We HAVE evidence of an association between age-group and whether a U.S. adult consumes 5 or more servings of fruits and veggies per day.

What are the conditions? CHECK ALL THAT APPLY. We have a random sample of 400 patients. We would have to assume that 400 is less than 10% of all patients. Since the sample size > 30, so we have a large enough sample, by the CENTRAL LIMIT THEOREM.

We have a random sample of 400 patients. We would have to assume that 400 is less than 10% of all patients. Since the sample size > 30, so we have a large enough sample, by the CENTRAL LIMIT THEOREM.

What is the probability? An important method for controlling the spread of the h6n2 influenza (bird flu) virus in chickens is having a procedure to determine whether chickens are infected with the virus. it is common to apply a procedure, called an elisa test, to measure the concentration of anti-bird flu antibodies in a blood sample taken from a chicken. if the elisa test reveals a high-enough concentration of antibodies, the chicken is said to test positive, and it is classified as infected with the virus. otherwise, the chicken is said to test negative, and it is classified as not infected. however, the elisa test is a complex procedure that is not always accurate. one type of mistake, a false positive result, occurs when the elisa test gives a positive result for a chicken that is not infected with the virus. a second type of mistake, a false negative result, occurs when the elisa test gives a negative result for an infected chicken. The ELISA test is known to have a probability of 0.05 of producing a false positive result and probability 0.10 of producing a false negative result for a single chicken. a) Suppose a veterinarian wishes to test a random sample from a very large flock of chickens at a commercial egg production farm. If 20 percent of the chickens in the flock are infected with the H6N2 virus and the other 80 percent are not infected, what is the probability that a single randomly selected chicken will test positive for H6N2? a) 0.22 b) 0.78 c) 0.11 d) 0.91

a) 0.22

The distribution of the diameters of a particular variety of oranges is approximately normal with a standard deviation of 0.3 inch. How does the diameter of an orange at the 67th percentile compare with the mean diameter? (A) 0.201 inch below the mean (B) 0.132 inch below the mean (C) 0.132 inch above the mean (D) 0.201 inch above the mean (E) 0.440 inch above the mean

The lengths of individual shellfish in a population of 10,000 shellfish are approximately normally distributed with mean 10 centimeters and standard deviation 0.2 centimeter. Which of the following is the shortest interval that contains approximately 4,000 shellfish lengths? (A) 0 cm to 9.949 cm (B) 9.744 cm to 10 cm (C) 9.744 cm to 10.256 cm (D) 9.895 cm to 10.105 cm (E) 9.9280 cm to 10.080 cm

(D) 9.895 cm to 10.105 cm

A consumer group is interested in estimating the proportion of packages of ground beef sold at a particular store that have an actual fat content exceeding the fat content stated on the label. How many packages of ground beef should be tested to estimate this proportion to within 3% with 96% confidence?

1172

How many degrees of freedom?

Professor Marge N. O'Vera wants to estimate the mean number of hours per week senior students at Podunk High School spend with their friends in person ( not texting or phoning). How many senior students must be randomly selected if she wants a 90% confidence level with a margin of error of no more than 1.5 hours. Previous studies have had a standard deviation of 4 hours.

What are the conditions? CHECK ALL THAT APPLY. 462 is less the 10% of all college freshmen. We have a random sample of college freshman. n*p-hat = 462*0.58 = 267.96 and n*(1-p-hat) = 462*0.42 = 194.04. These are both > 10.

462 is less the 10% of all college freshmen. We have a random sample of college freshman. n*p-hat = 462*0.58 = 267.96 and n*(1-p-hat) = 462*0.42 = 194.04. These are both > 10.

How many degrees of freedom? (n-2)

#1A: What is the ON CAMPUS proportion? (For this type of problem, to get full credit you must show both the ratio AND the decimal. If you forget the ratio, then you won't get credit.) A) 0.2121 B) 0.5152 C) 0.7273 D) 0.3731 E) 0.1791 F) 0.5522

C) 0.7273

Mrs. Sarah Bellum wants to know if the average homework load is different in the English and mathematics department at Podunk High School. She randomly selects 24 students. Twelve record the number of hours they spend during the semester on English homework and the other twelve record the number of hours they spend during the semester on math homework. Does there appear to be a significant difference in the mean homework load between the two departments? A) 2-proportion z-test B) matched pairs t-test C) matched pairs z-test D) 2-sample t-test

D) 2-sample t-test

Which of the following is a key distinction between well designed experiments and observational studies? A) More subjects are available for experiments than for observational studies. B) Ethical constraints prevent large-scale observational studies. C) Experiments are less costly to conduct than observational studies. D) An experiment can show a direct cause-and-effect relationship, whereas an observational study cannot. E) Tests of significance cannot be used on data collected from an observational study.

D) An experiment can show a direct cause-and-effect relationship, whereas an observational study cannot.

What are the hypotheses? Check all that apply Ha: p1 > p2 Ha: p1 < p2 Ho: p1 = p2 Ho: p1 = 0 and p2 = 0

Ha: p1 > p2 Ho: p1 = p2

Let X represent a random variable whose distribution is normal, with a mean of 100 and a standard deviation of 10. Which of the following is equivalent to P(X > 115) P(X < 115) P(X <= 115) P(X < 85) P(85 < X < 115) 1 - P(X < 85)

P(X < 85)

CONDITIONS. Check all that are true. The 100 volunteers were RANDOMLY ASSIGNED to the two groups. Normality - large counts condition Since this was an experiment, the 10% condition would not apply.

The 100 volunteers were RANDOMLY ASSIGNED to the two groups. Normality - large counts condition Since this was an experiment, the 10% condition would not apply.

4B - Check all that apply. b) Based on your conclusion in part (a), which type of error, Type I or Type II, is it possible? Describe the consequences of this error in the context of this study Type I Error Type II Error In REALITY, the new medication DOES NOT help to reduce stomach pain, but the company thinks it does and spends money to manufacture and sell a new drug. In REALITY, the new medication DOES help to reduce stomach pain, but the company fails to detect this and possibly ceases/delays the development of the new pain reliever.

Type II Error In REALITY, the new medication DOES help to reduce stomach pain, but the company fails to detect this and possibly ceases/delays the development of the new pain reliever.

An advertising agency in a large city is conducting a survey of adults to investigate whether there is an association between highest level of educational achievement and primary source for news. The company takes a random sample of 2500 adults in the city. The results are shown in the table below. b) If an adult is selected at random from this sample, what is the probability that the selected adult obtains news primarily from the internet? a) 0.3535 b) 0.1333 c) 0.8321 d) 0.1121

a) 0.3535

What is the z-score? a) 0.82 b) 0.55 c) 0.37 d) 0.95

a) 0.82

#3 - CALCULATE chi-square test statistic a) 8.9835 b) 9.5566 c) 7.5421 d) 2.9798

a) 8.9835

What are the null and alternative hypotheses? a) If the inference problem were a matched pairs t-test... H0 : Md = 0 Ha : Md > 0 b) If the inference problem were a 2-sample t-test... H0 : M1 = M2 Ha : M1 > M2

a) If the inference problem were a matched pairs t-test... H0 : Md = 0 Ha : Md > 0

Define the true MEAN(s) a) If the test is a 2-sample t-test... Mb = true mean length of adult fish, Buy-Rite Pets (inches) Mf = true mean length of adult fish, Fish Friends (inches) b) If the test is a matched pairs t-test... Mb = true mean length of adult fish, Buy-Rite Pets (inches) Mf = true mean length of adult fish, Fish Friends (inches) Md = Mb - Mf

a) If the test is a 2-sample t-test... Mb = true mean length of adult fish, Buy-Rite Pets (inches) Mf = true mean length of adult fish, Fish Friends (inches)

3B. More or less likely? (You would need to re-draw the normal model, calculate a z-score, and find the probability.) (b) The principals' association in the state suggests that instead of choosing one day at random, the state should choose 3 days at random. With the suggested plan, High School A would lose some of its state funding in the subsequent year if the mean number of students absent for the 3 days is greater than 140. Would High School A be more likely, less likely, or equally likely to lose funding using the suggested plan compared to the plan described in part (a)? Justify your choice. a) Less Likely b) More Likely

a) Less Likely

A carnival game allows the player a choice of simultaneously rolling two, four, six, eight, or ten fair dice. Each die has six faces numbered 1 through 6, respectively. After the player rolls the dice, the numbers that appear on the faces that land up are recorded. The player wins if the greatest number recorded is 1 or 2. How many dice should the player choose to roll to maximize the chance of winning? a) Two b) Four c) Six d) Eight e) Ten

a) Two

How do you calculate the z-score? b) The team's best time so far this season is 3:19:48 (= 199.48 seconds). What is the probability that the team will beat its own best time at the conference championship? a) z Score - option 1 z=obs-exp/stdev = 199.48-200.57/0.461 = -2.364 b) z Score - option 2 z=obs-exp/stdev = 200.57-199.48/0.461 = 2.634

a) z Score - option 1 z=obs-exp/stdev = 199.48-200.57/0.461 = -2.364

A least squares regression line was fitted to the weights (in pounds) versus age (in months) of a group of many young children. The equation of the line is y hat = 16.6+.65t where y hat is the predicted weight and t is the age of the child. A 20-month-old child in this group has an actual weight of 25 pounds. Which of the following is the residual weight, in pounds, for this child? a) 7.85 b) -4.60 c) 4.60 d) 5.00 e) 7.85

b) -4.60

What is the probability? b) The team's best time so far this season is 3:19:48 (= 199.48 seconds). What is the probability that the team will beat its own best time at the conference championship? a) 0.91 b) 0.002 c) 0.009 d) 0.554

c) 0.009

#3 - CALCULATE p-value a) 0.211 b) 0.0532 c) 0.0112 d) 0.9543

c) 0.0112

A mathematics competition uses the following scoring procedure to discourage students from guessing(choosing an answer randomly) on the multiple-choice questions. For each correct response, the score is 7. For each question left unanswered, the score is 2. For each incorrect response, the score is 0. If there are 5 choices for each question, what is the minimum number of choices that the student must eliminate before it is advantageous to guess among the rest? HINT: CAN YOU ELIMINATE ANY CHOICES? a) 0 b) 1 c) 2 d) 3 e) 4

c) 2

Each of the faces of a fair six-sided number cube is numbered with one of the numbers 1 through 6, with a different number appearing on each face. Two such numbers will be tossed, and the sum of the numbers appearing on the faces that land up will be recorded. What is the probability that the sum will be 4, given that the sum is less than or equal to 6? a) 2/36 b) 3/36 c) 3/15 d) 2/9 e) 4/6

c) 3/15

Suppose that the distribution of a set of scores has a mean of 47 and a standard deviation of 14. If 4 is added to each score, what will be the mean and the standard deviation of the distribution of new scores? A) 51 14 B) 51 18 C) 47 14 D) 47 16 E) 47 18

A) 51 14

4C. What is the STANDARD DEVIATION? (Round to 3 decimal places) Austin and Bonnie are friends that both work as waiters in two different restaurants. The amount of money that Austin earns in a week is a random variable with a mean of $450 and a standard deviation of $65. The amount of money that Bonnie earns in a week is a random variable with a mean of $580 and a standard deviation of $120. The two of them work in different parts of town, so we will assume that the two waiters' earnings are independent of one another. We will also assume that the distributions for each waiter's weekly earnings are approximately normally distributed. c) What are the mean and standard deviation for the mean difference (A - B), Austin's earnings and Bonnie's earnings for one week?

136.473

#2A. Show your work for the probability statement and the answer as a decimal! Round to four decimal places. Nine sales representatives, 6 men and 3 women, at a small company wanted to attend the national convention. There were only enough travel funds to send 3 people. The manager selected 3 people to attend and stated that the people were selected at random. The 3 people selected were women. There were concerns that no men were selected to attend the convention. a) Calculate the probability that randomly selecting 3 people from a group of 6 men and 3 women will result in selecting 3 women. A) 0.0370 B) 0.0119

B) 0.0119

If a random sample of 1,000 Austin residents contains 535 persons who prefer Time Warner internet to AT&T internet, is this sufficient evidence to conclude that more than half the people in Austin prefer Time Warner at the 0.01 level? A) 1-proportion z-interval B) 1-proportion z-test C) 2-proportion z-test D) 1-sample t-test

B) 1-proportion z-test

The dotplot below displays the total numbers of miles that the 28 residents of one street in a certain community traveled to work in one five-day work week. Which of the following is closest to the percentile rank of a resident from this street who traveled 85 miles to work that week? A) 60 B) 70 C) 75 D) 80 E) 85

B) 70

What are the hypotheses? a) p = true proportion of Austin residents who prefer Time Warner H0: p = 0.5 Ha: p > 0.5 b) mu = true mean number of Austin residents who prefer Time Warner H0: mu = 0.5 Ha: mu > 0.5

Use p (the true proportion)

#1 - CONDITIONS. Check all that apply We have a random sample of 10 pharmacies, which is less than 10% of ALL pharmacies. The conditions are met, so we can use a MATCHED PAIRS t-test with df=9. Normal Condition: Create a dotplot (or boxplot) of the active ingredient of the NAME BRAND and GENERIC BRAND The conditions are met, so we can use a 2-SAMPLE T-TEST with df = 17. 4659. Normal Condition: Create a dotplot (or boxplot) of the DIFFERENCES in active ingredient (name - generic) of the NAME BRAND and GENERIC BRAND

We have a random sample of 10 pharmacies, which is less than 10% of ALL pharmacies. The conditions are met, so we can use a MATCHED PAIRS t-test with df=9. Normal Condition: Create a dotplot (or boxplot) of the active ingredient of the NAME BRAND and GENERIC BRAND

What are the conditions? CHECK ALL THAT APPLY. We have a random sample of sites in a region of Madagascar. We would have to assume that 25 sites is less than 10% of all sites in Madagascar. The distribution of number of offspring is normally distributed (so the sample size doesn't matter)

We have a random sample of sites in a region of Madagascar. We would have to assume that 25 sites is less than 10% of all sites in Madagascar. The distribution of number of offspring is normally distributed (so the sample size doesn't matter)

CONDITIONS. Check all that apply. We have one random sample of 8866 U.S. adults. 8866 adults is less than 10% of all U.S. adults. All expected counts ≤ 5. All expected counts ≥ 5.

We have one random sample of 8866 U.S. adults. 8866 adults is less than 10% of all U.S. adults. All expected counts ≥ 5.

In this study, the child that spoke their first word at the youngest age was 7 months old when they spoke their first word. This child later had a Gesell score of 113. Calculate the residual for this child's score, and explain what this residual means in context. CHECK ALL THAT APPLY predicted score = 109.305 - 1.1933(7) = 100.9519 residual = observed score - predicted score = 113 - 100.9519 = 12.0481 This child's Gesell score was about 12 points higher than what THE LINEAR MODEL PREDICTS for a child who spoke their first word at this age. The linear model underestimated the score for this particular child.

predicted score = 109.305 - 1.1933(7) = 100.9519 residual = observed score - predicted score = 113 - 100.9519 = 12.0481 This child's Gesell score was about 12 points higher than what THE LINEAR MODEL PREDICTS for a child who spoke their first word at this age. The linear model underestimated the score for this particular child.

Each of 100 laboratory rats has available both plain water and a mixture of water and caffeine in their cages After 24 hours, two measures were recorded for each rat the amount of caffeine the rat consumed. X, and the rat's Wood pressure, Y. The correlation between x and y was 0.428. Which of the following conclusions is justified on the basis of this study? (a) The correlation between X and Y in the population of rats is also 0.428. (b) If the rats stop drinking the water/caffeine mixture, this would cause a reduction in their blood pressure. (c) About 18 percent of the variation in blood pressure can be explained by a linear relationship between blood pressure and caffeine consumed. (d) Rats with lower blood pressure do not like the water/caffeine mixture as much as do rats with higher blood pressure. (e) Since the correlation is not very high, the relationship between the amount of caffeine consumed and blood pressure is not linear.

(c) About 18 percent of the variation in blood pressure can be explained by a linear relationship between blood pressure and caffeine consumed.

#3C. What is the probability? (Round to 3 decimal places.) A typical school week consists of the days Monday, Tuesday, Wednesday, Thursday, and Friday. The principal at High School A believes that the number of absences tends to be greater on Mondays and Fridays, and there is concern that the school will lose state funding if the attendance count occurs on a Monday or Friday. If one school day is chosen at random from each of 3 typical school weeks, what is the probability that none of the 3 days chosen is a Tuesday, Wednesday, or Thursday?

0.064

#4A. What is the mean? Austin and Bonnie are friends that both work as waiters in two different restaurants. The amount of money that Austin earns in a week is a random variable with a mean of $450 and a standard deviation of $65. The amount of money that Bonnie earns in a week is a random variable with a mean of $580 and a standard deviation of $120. The two of them work in different parts of town, so we will assume that the two waiters' earnings are independent of one another. We will also assume that the distributions for each waiter's weekly earnings are approximately normally distributed. a) What are the mean and standard deviation for Austin and Bonnie's combined earnings (A + B) for one week?

1030

What would the graph for the conditions look like? A)Dotplot of BOTH English and Math scores. B)Dotplot of the differences

A)Dotplot of BOTH English and Math scores.

Pick the sewing machine that affects the appropriateness of using a linear regression model The scatterplot below displays the price in dollars and quality rating for 14 different sewing machines. (b) One of the 14 sewing machines substantially affects the appropriateness of using a linear regression model to predict quality rating based on price. Report the approximate price and quality rating of that machine and explain your choice. A) The point at $500 and 81 quality rating B) The point at $200 and 40 quality rating C) The point at $175 and 65 quality rating D) The point at $2200 and a 65 quality rating

D) The point at $2200 and a 65 quality rating

Since many individuals walk around their homes in their socks, a manufacturer has created a material for socks that is believed to be more resistant to wear than cotton. The manufacturer wishes to test this belief over a period of a month. Given a group of volunteers, which of the following designs will best test this new material's resistance to wear? A) have the volunteers wear the socks made from the new material for a month, and check the wear on the socks at the end of the month. B) Allow half of the volunteers to wear cotton socks, while the other half wear socks made of the new material. Compare the wear on the socks at the end of the month. C) Randomly assign half of the volunteers to wear cotton socks, while the other half wear socks made of the new material. Compare the wear on the socks at the end of the month. D) Randomly assign half of the volunteers to wear cotton socks, while the other half wear socks made of the new material. At the end of two weeks, the volunteers should change sock types. Compare the wear on the socks at the end of the month. E) For each volunteer, randomly choose which foot wears a cotton sock, while the other foot wears a sock made of the new material. Compare the wear on the socks at the end of the month.

E) For each volunteer, randomly choose which foot wears a cotton sock, while the other foot wears a sock made of the new material. Compare the wear on the socks at the end of the month.

CONCLUSION. Check all that apply. Assume alpha = 0.05. Since our p-value is less than alpha... Since our p-value is greater than alpha... we REJECT Ho. we FAIL TO REJECT Ho. We HAVE evidence to show that the MEAN length of adult fish from Fish Friends is GREATER than the mean length of adult fish from Buy-Rite Pets. We LACK evidence to show that the MEAN length of adult fish from Fish Friends is GREATER than the mean length of adult fish from Buy-Rite Pets.

Since our p-value is greater than alpha... we FAIL TO REJECT Ho. We LACK evidence to show that the MEAN length of adult fish from Fish Friends is GREATER than the mean length of adult fish from Buy-Rite Pets.

Assume alpha is 10%. What can you CONCLUDE about this p-value? Since our p-value is less than alpha... Since our p-value is greater than alpha.... we REJECT Ho. we FAIL TO REJECT Ho. We HAVE evidence to show that the new pain reliever helps reduce the proportion of patients with stomach irritation. We LACK evidence to show that the new pain reliever helps reduce the proportion of patients with stomach irritation.

Since our p-value is greater than alpha.... we FAIL TO REJECT Ho. We LACK evidence to show that the new pain reliever helps reduce the proportion of patients with stomach irritation.

CHECK ALL THAT APPLY The scatterplot below displays the price in dollars and quality rating for 14 different sewing machines. Quality Rating 40 50 60 70 80 Price (dollars) $500 $2.000 $2,500 $1,000 $1,500 (a) Describe the nature of the association between price and quality rating for the sewing machines. The association between PRICE and QUALITY RATING appears to be: fairly weak moderately strong positive linear non-linear If we remove the point on the far right, the a linear model may be appropriate.

The association between PRICE and QUALITY RATING appears to be: fairly weak positive non-linear If we remove the point on the far right, the a linear model may be appropriate.

WHAT IS THE STANDARD DEVIATION of X? Each full carton of Grade A eggs consists of 1 randomly selected empty cardboard container and 12 randomly selected eggs. The weights of such full cartons are approximately normally distributed with a mean of 840 grams and a standard deviation of 7.9 grams. The weights of the empty cardboard containers have a mean of 20 grams and a standard deviation of 1.7 grams. It is reasonable to assume independence between the weights of the empty cardboard containers and the weights of the eggs. It is also reasonable to assume independence among the weights of the 12 eggs that are randomly selected for a full carton. Let the random variable X be the weight of a single randomly selected Grade A egg. (b) What is the standard deviation of X? a) 2.2271 b) 1.4432 c) 7.3322 d) 2.9778

a) 2.2271

A wildlife biologist is interested in the relationship between the number of chirps per minute for crickets (y) and temperature. Based on the collected data, the least-squares regression line is y x ˆ = + 10.53 3.41 , where x is the number of degrees Fahrenheit by which the temperature exceeds 50°. Which of the following best describes the meaning of the slope of the least squares regression line? (A) For each increase in temperature of 1 degree Fahrenheit, the estimated number of chirps per minute increases by 10.53 (B) For each increase in temperature of 1 degree Fahrenheit, the estimated number of chirps per minute increases by 3.41 (C) For each increase of one chirp per minute, there is an estimated increase in temperature of 10.53 degrees Fahrenheit (D) For each increase of one chirp per minute, there is an estimated increase in temperature of 10.53 degrees Fahrenheit (E) The slope has no meaning because the units of measure for x and y are not the same.

(B) For each increase in temperature of 1 degree Fahrenheit, the estimated number of chirps per minute increases by 3.41

The weight, in pounds, of a full backpack and the corresponding number of books in the backpack were recorded for each of 10 college students. The resulting data were used to create the residual plot and the regression output shown below Number of Books Residual Parameter Estimate Std. Er. Alternative DF T Stat P-Value Intercept 10.53 1.23 not equal 0 8 8.57 <0.0001 Slope 0.53 0.46 not equal 0 8 1.15 0.2825 Which of the following values is closest to the actual weight, in pounds of the backpack for the student who had 4 books in the backpack? (A) 8 (B) 10 (C) 13 (D) 15 (E) 17

(D) 15

A delivery service places packages into large containers before flying them across the country. These filled containers vary greatly in their weight. Suppose the delivery service's airplanes always transport two such containers on each flight. The two containers are chosen so their combined weight is close to, but does not exceed, a specified weight limit. A random sample of flights with these containers is taken, and the weight of each of the two containers on each selected flight is recorded. The weights of the two containers on the same flight (a) will have a correlation of 0 (b) will have a negative correlation (c) will have a positive correlation that is less than 1 (d) will have a correlation of 1 (e) cannot be determined from the information given

(b) will have a negative correlation

choose one What would change in your procedure for the previous problem if the random sample contained only 10 patients? What additional information would you need to meet your assumptions? A) Since that sample size is less than 30, we would need to see a graph of the sample data, to check for plausible normality (hopefully no extreme outliers or obvious skewness). B) The procedure doesn't need to be changed. C) Check if the number of successes and number of failures are both > 10.

A) Since that sample size is less than 30, we would need to see a graph of the sample data, to check for plausible normality (hopefully no extreme outliers or obvious skewness).

#4A. What is the standard deviation? (Round to 3 decimal places) Austin and Bonnie are friends that both work as waiters in two different restaurants. The amount of money that Austin earns in a week is a random variable with a mean of $450 and a standard deviation of $65. The amount of money that Bonnie earns in a week is a random variable with a mean of $580 and a standard deviation of $120. The two of them work in different parts of town, so we will assume that the two waiters' earnings are independent of one another. We will also assume that the distributions for each waiter's weekly earnings are approximately normally distributed. a) What are the mean and standard deviation for Austin and Bonnie's combined earnings (A + B) for one week?

136.473

A sample of 481 historians responded to questions about the performance of various U.S. presidents, and the results were presented at the annual conference of the Organization of American Historians (Associated Press, March 28, 1991). Of the 481 surveyed, 433 responded that Ronald Reagan lacked the proper intellect for the presidency. Construct a 90% confidence interval for the true proportion of all historians who believe that Reagan lacked the proper intellect for the presidency. (Note: We are assuming that the 481 historians were chosen randomly.) A) 1-proportion z-interval B) 1-proportion z-test C) 1-sample t-interval

A) 1-proportion z-interval

A psychologist finds that fidgety patients tap their fingers on average 500 times during a 2 hour period. They wish to test if this is still true for the same patients, but in a room decorated with soothing colors and soft lighting. They believe that a warmly decorated room may alter the fidgeting behavior, causing subjects to tap their fingers less than they do under normal conditions. A random sample of 400 patients has a mean of 420 taps and a standard deviation of 60 taps in a 2 hour period. Test the claim at the 0.05 significance level. A) 1-sample t-test B) 1-proportion z-test C) 1-sample t-interval D) 2-proportion z-test E) Matched Pairs t-test

A) 1-sample t-test

What type of inference? A traffic study interested in color preferences asked two separate samples of drivers - one of truck drivers, and another of drivers in sports cars - which of the three colors(yellow, red, green) they least like.Does there seem to be a difference in the relative distribution (breakdown of proportions) of color preferences between drivers of trucks and drivers of sports cars? red green yellow Trucks 27 14 26 Sports Cars 28 18 20 A) Chi-squared Test of Homogeneity B) Chi-squared Goodness of Fit C) Chi-squared Test of Independence

A) Chi-squared Test of Homogeneity

Interpret the slope of this regression equation. Does the age at which a child begins to talk predict a later score on a test of mental ability? As study of the development of young children recorded the age in months at which each of 21 children spoke their first word and their Gesell Adaptive Score, the result of an aptitude test taking much later. predicted score = 109.305 -1.1933(age) A) For each additional month that it takes a child to speak their first word, THE LINEAR MODEL PREDICTS that their Gesell score will DECREASE by 1.1933 points. B) For each additional month that it takes a child to speak their first word, THE LINEAR MODEL PREDICTS that their Gesell score will INCREASE by 1.1933 points. C) For each additional month that it takes a child to speak their first word, their Gesell score will DECREASE by 1.1933 points.

A) For each additional month that it takes a child to speak their first word, THE LINEAR MODEL PREDICTS that their Gesell score will DECREASE by 1.1933 points.

(c) Chris is interested in buying one of the 14 sewing machines. He will consider buying only those machines for which there is no other machine that has both higher quality and lower price. On the scatterplot reproduced below, circle all data points corresponding to machines that Chris will consider buying A) Option 1 B) Option 3 C) Option 2 D) Option 4

A) Option 1

Interpret the y-intercept of the regression equation. Comment on this observation. A) When a child speaks their first word at age zero months, THE MODEL PREDICTS a Gesell score will be about 109. Since this is reaching beyond the ends of the linear model (the youngest age recorded in this study is 7 months), this is extrapolation and is not a useful prediction. B) For each additional month that it takes a child to speak their first word, THE LINEAR MODEL PREDICTS that their Gesell score will DECREASE by 1.1933 points. C) For each additional month that it takes a child to speak their first word, THE LINEAR MODEL PREDICTS that their Gesell score will INCREASE by 1.1933 points.

A) When a child speaks their first word at age zero months, THE MODEL PREDICTS a Gesell score will be about 109. Since this is reaching beyond the ends of the linear model (the youngest age recorded in this study is 7 months), this is extrapolation and is not a useful prediction.

To estimate the mean number of young animals per herd of mouse lemurs, a biologist randomly selects sites in a region of Madagascar and counts the young members of herds sighted near the chosen location. The mean from 25 sites is 8.2, with a standard deviation of 3.4. If the count of offspring is normally distributed, find an 80% confidence interval for the mean number of young per herd. A) 1-proportion z-interval B) 1-sample t-interval (means)

B) 1-sample t-interval (means)

A group of 20 students participated in a horsepower lab, in which each student recorded the amount of time it took to run up a full flight of stairs. Each student then calculated the horsepower that they generated, and the following linear model was produced to predict horsepower based on the time required to run up the stairs: predicted horsepower = 153 - 0.320(time) One student in the group recorded a time of 2.10 seconds, and the residual for this student's horsepower was +0.432. What was this student's observed horsepower? A) 0.858 B) 1.290 C) 0.446 D) 0.412 E) 2.202

B) 1.290

A research study conducted by a group of psychologists at Podunk University (PU) states that there is a correlation between the number of novels read per year by college students and the number of dates that those students go on each month. If "number of novels" read per year is used as the explanatory variable in this regression analysis, which of the following is the best interpretation of a positive residual value for one student's data? A) The model overestimates the number of dates that this student goes on each month. B) The model underestimates the number of dates that this student goes on each month. C) The model overestimates the number of novels read by this student during the year. D) The model underestimates the number of novels that this student read during the year. E) There is a negative association between number of novels read per year and the number of dates per month

B) The model underestimates the number of dates that this student goes on each month.

Let's say that 58% of 462 randomly selected college freshman (from colleges across the nation) reported being overwhelmed by the task of managing their time. (No one is there to nag them about allowing adequate time to study, do laundry, sleep, or get to class.) Construct and interpret a 90% confidence interval for n, the true proportion of college freshman that are overwhelmed by the task of managing their own time. A) 1-proportion z-test B) 2-proportion z-test C) 1-proportion z-interval D) 2-proportion z-interval

C) 1-proportion z-interval

A high school physics teacher was conducting an experiment with his class on the length of time it will take a marble to roll down a sloped chute. The class ran repeated trials in order to determine the relationship between the length, in centimeters, of the sloped chute and the time, in seconds, for the marble to roll down the chute. A linear relationship was observed and the correlation coefficient was 0.964. After discussing their results, the teacher instructed toe students to convert all of the length measurements to meters but leave the time in seconds. What effect will this have on the correlation of the two variables? A) Because the standard deviation of the lengths in meters will be one hundredth of the standard deviation of the lengths in centimeters, the correlation will decrease by one hundredth to 0.954 B) Because the standard deviation of the lengths in meters will be one hundredth of the standard deviation of the lengths in centimeters, the correlation will decrease proportionally to 0.00964 C) Because hanging from centimeters to meters does not affect the value of the correlation, the correlation will remain 0.964. D) Because only the length measurements have been changed, the correlation will decrease substantially E) Because meters are a much more common measurement for length in determining speed, the linear relationship of the data will be stronger and thus the correlation will increase substantially.

C) Because hanging from centimeters to meters does not affect the value of the correlation, the correlation will remain 0.964.

In a recent survey, 60 randomly selected married couples from the same town were asked to rate the overall quality of living in their town on a scale from 1 (very poor) to 10 (excellent) on twenty different attributes such as accessibility to major highways, availability of entertainment, services provided by tax dollars, etc. For each couple,the husband's individual ratings on the twenty attributes were averaged to produce an overall quality rating, and that process was repeated for the wife. Each point on the scatterplot below displays the overall rating of one of the 60 couples with the husband's rating represented by the horizontal axis and the wife's rating represented by the vertical axis.Based on the scatterplot, which of the following statements is true? A) The range in the husbands' overall ratings is greater than the range in the wives' overall ratings. B) More overall ratings of 7 or less were assigned by husbands than by wives. C) Husbands tended to rate the quality of living higher than their wives did. D) For each couple, the overall rating assigned by the husband was the same as the overall rating assigned by the wife. E) The difference in overall ratings between a husband and wife was not more than 3 for any couple.

C) Husbands tended to rate the quality of living higher than their wives did.

What are the hypotheses? A) mu = true mean number of finger taps during a 2-hour period for all patients H0: mu = 500 Ha: mu < 500 Do you use mu? B) p= true mean number of finger taps during a 2-hour period for all patients H0: p = 500 Ha: p < 500 Do you use p?

Do you use mu?

The histogram below displays the times in minutes, needed for each chimpanzee in a sample of 26 to complete a simple navigation task. It was determined that the largest observation, 93, is an outlier since Q3 + 1.5(Q3-Q1) = 87.125. Which of the following boxplots could represent the information in the histogram? A B C D E

A scatterplot is created the weight and height data of 36 students in an AP Statistics class. Originally, the weight of each student was measured in pounds, and height was measured in inches. If each student's weight is converted from pounds to kilograms, and each student's height is also converted from inches to centimeters, which of the following statements is/are true? I. The correlation coefficient will remain unchanged. II. The slope of the regression line (for weight vs. height) will remain unchanged. III. The z-score for each student's height measurement will remain unchanged. A) I only B) II only C) III only D) I and II E) I and III

E) I and III

The responses of the 100 students are summarized in the segmented bar graph shown. b) Write a few sentences summarizing what the graph reveals about the association between residential status and level of participation in extracurricular activities among the 100 students in the sample. Choose ALL the apply Off-campus students are more likely to NOT be involved in any extracurricular activities. Off-campus students are more likely to NOT be involved in any extracurricular activities than on-campus students. (by about 15 percentage points) On-campus students are MUCH more likely to be involved in one activity, and SLIGHTLY more likely to be involved in 2 or more activities. On-campus students are MUCH more likely to be involved in one activity, and SLIGHTLY more likely to be involved in 2 or more activities than off-campus students.

Off-campus students are more likely to NOT be involved in any extracurricular activities than on-campus students. (by about 15 percentage points) On-campus students are MUCH more likely to be involved in one activity, and SLIGHTLY more likely to be involved in 2 or more activities than off-campus students.

Explain why you made this choice. CHOOSE ALL THAT APPLY. This point is to the far RIGHT of all the other points. This point would have a large NEGATIVE residual value. This is an INFLUENTIAL POINT. It greatly affects the correlation. This is an INFLUENTIAL POINT. It doesn't affect the correlation With this point, the association between price and quality rating appears CURVED. Without this point, a positive (albeit weak) linear association seems appropriate. With this point, the association between price and quality rating appears LINEAR. Removing it will not affect the linear regression model.

This point is to the far RIGHT of all the other points. This point would have a large NEGATIVE residual value. This is an INFLUENTIAL POINT. It greatly affects the correlation. With this point, the association between price and quality rating appears CURVED. Without this point, a positive (albeit weak) linear association seems appropriate.

What are the conditions? Check all that apply! We have a random sample of 24 students from two independent groups. NORMALITY? Since the sample sizes are both < 30, you must make graphs (dotplots or boxplots) of each group. The graphs are roughly normal; each graph has no obvious outliers.

We have a random sample of 24 students from two independent groups. NORMALITY? Since the sample sizes are both < 30, you must make graphs (dotplots or boxplots) of each group. The graphs are roughly normal; each graph has no obvious outliers.

What are the conditions? CHECK ALL THAT APPLY. We have separate random samples of drivers. Both the sample of trucks and cars are less than 10% of the respective population. All expected values are greater than or equal to 5.

We have separate random samples of drivers. Both the sample of trucks and cars are less than 10% of the respective population. All expected values are greater than or equal to 5.

CONDITIONS. Check all that apply. We have two SEPARATE random samples of fish from both stores. Normal Condition: boxplots (both stores) Normal Condition: boxplot of the differences Since the boxplots (of both stores) looks roughly symmetric, and there are NO OUTLIERS, normality is plausible for BOTH populations of fish. Since the boxplot of the differences looks roughly symmetric, and there are NO OUTLIERS, normality is plausible for the DIFFERENCES in fish lengths populations of fish.

We have two SEPARATE random samples of fish from both stores. Normal Condition: boxplots (both stores) Since the boxplots (of both stores) looks roughly symmetric, and there are NO OUTLIERS, normality is plausible for BOTH populations of fish.

The distribution of colors of candies in a bag is as follows. Color Brown Red Yellow Green Orange Proportion 0.3 0.2 0.2 0.2 0.1 If two candies are randomly drawn from the bag with replacement, what is the probability that they are the same color? a) 0.09 b) 0.22 c) 0.25 d) 0.75 e) 0.78

b) 0.22

Define the true MEAN(s) a) Define true mean of name brand and true mean of generic brand b) Find the true mean difference of (name brand - generic brand)

b) Find the true mean difference of (name brand - generic brand)

#3A. Calculate the z-Score Schools in a certain state receive funding based on the number of students who attend the school. To determine the number of students who attend a school, one school day is selected at random and the number of students in attendance that day is counted and used for funding purposes. The daily number of absences at High School A in the state is approximately normally distributed with mean of 120 students and standard deviation of 10.5 students. (a) If more than 140 students are absent on the day the attendance count is taken for funding purposes, the school will lose some of its state funding in the subsequent year. Approximately what is the probability that High School A will lose some state funding? a) z = -1.09476 b) z = 1.09476

b) z = 1.09476

WHAT IS THE MEAN of X? Each full carton of Grade A eggs consists of 1 randomly selected empty cardboard container and 12 randomly selected eggs. The weights of such full cartons are approximately normally distributed with a mean of 840 grams and a standard deviation of 7.9 grams. The weights of the empty cardboard containers have a mean of 20 grams and a standard deviation of 1.7 grams. It is reasonable to assume independence between the weights of the empty cardboard containers and the weights of the eggs. It is also reasonable to assume independence among the weights of the 12 eggs that are randomly selected for a full carton. Let the random variable X be the weight of a single randomly selected Grade A egg. (a) What is the mean of X? a) 78.32 b) 91.22 c) 68.33 d) 51.29

c) 68.33

Name the inference test The Behavioral Risk Factor Surveillance System is an ongoing health survey system that tracks health conditions and risk behaviors in the United States. In one of their studies, a random sample of 8,866 adults answered the question "Do you consume five or more servings of fruits and vegetables per day?" The data are summarized by response and by age-group in the frequency table below. Age-Group(years) Yes No Total 18-34 231 741 972 35-54 669 2,242 2,911 55 or older 1,291 3,692 4,983 Total 2,191 6,675 8,866 Does the data provide convincing statistical evidence that there is an association between age-group and whether or not a person consumes five or more servings of fruits and vegetables per day for adults in the United States? a) Chi squared Test of Homogeneity b) Chi squared Goodness of Fit c) Chi squared Test of Independence

c) Chi squared Test of Independence

Given mu1 and mu2 defined in the picture, how would you write the hypotheses? M1 = true mean number of hours spent on English HW by all Westwood students this semester M2 = Math HW a) Option 1 H0: M1 not equal to M2 Ha: M1 = M2 b) Option 2 H0: M1 = M2 Ha: M1 < M2 c) Option 3 H0: M1 = M2 Ha: M1 not equal to M2 d) Option 4 H0: M1 = M2 Ha: M1 > M2

c) Option 3 H0: M1 = M2 Ha: M1 not equal to M2

b) Let us assume that during a Saturday afternoon, the donut stand gets 50 customers in a busy hour. The owner of the donut stand has to determine whether they will be able to make enough money to pay "rent" to the city, and would like to make at least $320 during this busy hour. How likely is it that the stand makes a total of at least $320 from a sample of 50 customers? a) 0.127 b) 0.0051 c) 0.333 d) 0.0007

d) 0.0007

In a certain school, 17 percent of the students are enrolled in a psychology course, 28 percent are enrolled in a foreign language course, and 32 percent are enrolled in either a psychology course or a foreign language course or both. What is the probability that a student chosen at random from this school will be enrolled in both a foreign language course and a psychology course? a) 0.45 b) 0.32 c) 0.20 d) 0.13 e) 0.05

d) 0.13

What is the p-value? a) 0.3112 b) 0.7551 c) 0.2487 d) 0.2049

d) 0.2049

Name the inference test A drug company currently sells a prescription pain reliever that has been shown to be effective at lowering arthritis pain. However, since the drug causes stomach irritation in some patients, the company has created a new formulation that it hopes will reduce this side effect. To see if the new formulation reduces the occurrence of stomach irritation for users of the pain reliever, the company conducted a small preliminary study to compare the new formulation with the current pain reliever. In the preliminary study of 100 subjects with arthritis, 50 were randomly assigned to take the current pain reliever and 50 were randomly assigned to take the new formulation. Patient responses at the end of the study are summarized in the table below. Patient Response Current Pain Reliever New Formulation Total Had stomach irritation 21 17 38 Had no stomach irritation 29 33 62 Total 50 50 100 Does the data from the preliminary study indicate, at the 10 percent level of significance, that the new formulation helps to reduce the proportion of patients with stomach irritation compared to the current pain reliever? a) 2-sample t-test b) 2-sample z-test c) matched pairs t-test d) matched pairs z-test e) 2-proportion z-test f)2-proportion t-test

e) 2-proportion z-test

What are the conditions? Check all that apply! n*p-hat = 535, and n*(1-phat) = 465, which are both at least 10. We have a random sample of Austin residents. 1000 residents is less than 10% of all Austin residents.

n*p-hat = 535, and n*(1-phat) = 465, which are both at least 10. We have a random sample of Austin residents. 1000 residents is less than 10% of all Austin residents.

Define the true proportions. Check all that apply p1 = true proportion of ALL patients on CURRENT pain reliever that experience stomach pain p2 = true proportion of ALL patients on NEW pain reliever that experience stomach pain

p1 = true proportion of ALL patients on CURRENT pain reliever that experience stomach pain p2 = true proportion of ALL patients on NEW pain reliever that experience stomach pain

A local real estate magazine used the median instead of the mean when it reported the SAT score of the average student who attends Groveland High School. A graphical display of SAT scores of students who attend Groveland High School indicated that the data were strongly skewed to the right. Which of the following explains why, in this situation, the median is a more accurate indicator of the SAT score of the average student than the mean is? (A) The mean is affected by the skewness, whereas the median is not. (B) The median is always the preferred statistic. (C) The mean will be less than the median when the data are strongly skewed to the right. (D) The mean should be used only when data are strongly skewed to the left. (E) The median is equal to one-half the sum of the maximum and minimum SAT scores at Groveland High.

(A) The mean is affected by the skewness, whereas the median is not.

A certain type of remote control car has a fully charged battery at the time of purchase. The distribution of running times of cars of this type, before they require recharging of the battery for the first time after its period of initial use, is approximately normal with a mean of 80 minutes and a standard deviation of 2.5 minutes. The Shaded area in the figure below represents which of the following probabilities? (A) The probability that the running time of a randomly-selected car of this type, before it requires recharging of the battery for the first time after its period of initial use is between 75 minutes and 82.5 minutes. (B) The probability that the running time of a randomly-selected car of this type, before it requires recharging of the battery for the first time after its period of initial use is between 75 minutes and 85 minutes. (C) The probability that the running time of a randomly-selected car of this type, before it requires recharging of the battery for the first time after its period of initial use is between 77.5 minutes and 82.5 minutes. (D) The probability that the running time of a randomly-selected car of this type, before it requires recharging of the battery for the first time after its period of initial use is between 77.5 minutes and 85 minutes. (E) The probability that the running time of a randomly-selected car of this type, before it requires recharging of the battery for the first time after its period of initial use is between 77.5 minutes and 87.5 minutes.

(A) The probability that the running time of a randomly-selected car of this type, before it requires recharging of the battery for the first time after its period of initial use is between 75 minutes and 82.5 minutes.

A small town employs 34 salaried, nonunion employees. Each employee receives an annual salary increase of between $500 and $2000 based on a performance review by the mayor's staff. Some employees are members of the mayor's political party, and the rest are not. Students at the local high school form two lists, A and B, one for the raises granted to employees who are in the mayor's party, and the other for raises granted to employees who are not. They want to display a graph (or graphs) of the salary increases in the student newspaper that readers can use to judge whether the two groups of employees have been treated in a reasonably equitable manner. Which of the following displays is LEAST likely to be useful to readers for this purpose? (A) Back-to-back stemplots of A and B (B) Scatterplot of B versus A (C) Parallel boxplots of A and B (D) Histograms of A and B that are drawn to the same scale (E) Dotplots of A and B that are drawn to the same scale

(B) Scatterplot of B versus A

A researcher has conducted a survey using a simple random sample of 50 registered voters to create a confidence interval to estimate the proportion of registered voters favoring the election of a certain candidate for mayor. Assume that a sample proportion does not change. Which of the following best describes the anticipated effect on the width of the confidence interval if the researcher were to survey a random sample of 200, rather than 50, registered voters? (A) The width of the new interval would be about one-fourth the width of the original interval. (B) The width of the new interval would be about one-half the width of the original interval. (C) The width of the new interval would be about the same width as the original interval. (D) The width of the new interval would be about twice the width of the original interval. (E) The width of the new interval would be about four times the width of the original interval.

(B) The width of the new interval would be about one-half the width of the original interval.

The statistics below provide a summary of the distribution of the heights, in inches, for a simple random sample of 200 young children. Mean: 46 inches Median: 45 inches First Quartile: 43 inches Standard Deviation: 3 inches Third Quartile: 48 inches (A) less than 43 inches (B) less than 48 inches (C) between 43 and 48 inches (D) between 40 and 52 inches (E) more than 46 inches

Math students across the country take an end-of-year exam late in the spring that is scored on a scale of 1 to 108.The distribution of scores has a mean of 72 and a median of 61. One would expect the shape of the distribution to be (A) unimodal and roughly symmetric (B) skewed to the left (C) skewed to the right (D) uniform (E) triangular

In the display of distributions A and B, which has the larger mean and which has the larger standard deviation? (A) Larger mean, A; larger standard deviation, A (B) Larger mean, A; larger standard deviation, B (C) Larger mean, B; larger standard deviation, A (D) Larger mean, B; larger standard deviation, B (E) Larger mean, B; same standard deviation

(D) Larger mean, B; larger standard deviation, B

The stemplot below shows the yearly earnings per share of stock for two different companies over a sixteen-year period. Which of the following statements is true? (A) The median of the earnings of Company A is less than the median of the earnings of the Company B. (B) The range of the earnings of Company A is less than the range of the earnings of Company B. (C) The third quartile of Company A is smaller than the third quartile of Company B. (D) The mean of the earnings of Company A is greater than the mean of the earnings of Company B. (E) The interquartile range of Company A is twice the interquartile range of Company B.

(D) The mean of the earnings of Company A is greater than the mean of the earnings of Company B.

The weights of a population of adult male gray whales are approximately normally distributed with a mean weight of 18,000 kilograms and a standard deviation of 4,000 kilograms. The weights of a population of adult male humpback whales are approximately normally distributed with a mean weight of 30,000 kilograms and a standard deviation of 6,000 kilograms. A certain adult male gray whale weighs 24,000 kilograms. This whale would have the same standardized weight (z-score) as an adult male humpback whale whose weight, in kilograms, is equal to which of the following? (A) 21,000 (B) 24,000 (C) 30,000 (D) 36,000 (E) 39,000

(E) 39,000

A botanist is studying the petal lengths, measured in millimeters, of two species of lilies. The box plots above illustrate the distribution of petal lengths from two samples of equal size, one from species A and the other from species B. Based on these box plots, which of the following is a correct conclusion about the data collected in this study? (A) The interquartile ranges are the same for both samples. (B) The range for species B is greater than the range for species A. (C) There are more petal lengths that are greater than 70 mm for species A than there are for species B. (D) There are more petal lengths that are greater than 40 mm for species B than there are for species A. (E) There are more petal lengths that are less than 30 mm for species B than there are for species A.

(E) There are more petal lengths that are less than 30 mm for species B than there are for species A.

In which of the following situations would it be most difficult to use a census? (A) To determine what proportion of licensed bicycles on a university campus have lights (B) To determine what proportion of students in a high school support wearing uniforms (C) To determine what proportion of registered students enrolled in a college are employed more than 20 hours each week (D) To determine what proportion of single-family dwellings in a small town have two-car garages (E) To determine what proportion of fish in Lake Michigan are bass

(E) To determine what proportion of fish in Lake Michigan are bass

4C. What is the MEAN? (Round to 3 decimal places) Austin and Bonnie are friends that both work as waiters in two different restaurants. The amount of money that Austin earns in a week is a random variable with a mean of $450 and a standard deviation of $65. The amount of money that Bonnie earns in a week is a random variable with a mean of $580 and a standard deviation of $120. The two of them work in different parts of town, so we will assume that the two waiters' earnings are independent of one another. We will also assume that the distributions for each waiter's weekly earnings are approximately normally distributed. c) What are the mean and standard deviation for the mean difference (A - B), Austin's earnings and Bonnie's earnings for one week?

-130

4B. Probability? (Round to 4 decimal places, assuming the z-score is 1.25) Austin and Bonnie are friends that both work as waiters in two different restaurants. The amount of money that Austin earns in a week is a random variable with a mean of $450 and a standard deviation of $65. The amount of money that Bonnie earns in a week is a random variable with a mean of $580 and a standard deviation of $120. The two of them work in different parts of town, so we will assume that the two waiters' earnings are independent of one another. We will also assume that the distributions for each waiter's weekly earnings are approximately normally distributed. b) What is the probability that Austin and Bonnie's combined weekly income exceeds $1200?

.1056

4D. What is the probability that Austin's weekly income is GREATER than Bonnie's weekly income? (Round the probability to 4 decimal places) Austin and Bonnie are friends that both work as waiters in two different restaurants. The amount of money that Austin earns in a week is a random variable with a mean of $450 and a standard deviation of $65. The amount of money that Bonnie earns in a week is a random variable with a mean of $580 and a standard deviation of $120. The two of them work in different parts of town, so we will assume that the two waiters' earnings are independent of one another. We will also assume that the distributions for each waiter's weekly earnings are approximately normally distributed. d) What is the probability that Austin's weekly income is greater than Bonnie's weekly income?

.1704

Which of the following inference procedures automatically include blocking as part of the design? A) Austin high school students getting between 7 and 8 hours of sleep per night score higher on tests over their curriculum. B) Students in the United States who get between 7 and 8 hours of sleep per night get better grades. C) Austin students who sleep between 7 and 8 hours per night get better grades. D) High school students getting between 7 and 8 hours of sleep per night score higher on tests over their curriculum. E) Since a placebo was not included in the study, no significant conclusions can be made.

A) Austin high school students getting between 7 and 8 hours of sleep per night score higher on tests over their curriculum.

Ann Landers - who wrote a daily advice column appearing in newspapers across the country - once asked her readers, "If you had it to do over again, would you have children?" Of the more than 10,000 readers who responded, 70% said no. (I'm certain your parents would say yes!) What does this show? A) The survey is meaningless because of voluntary response bias. B) No meaningful conclusion is possible without knowing something more about the characteristics of her readers. C) The survey would have been more meaningful if she had picked a random sample of the 10,000 readers who responded. D) The survey would have been meaningful if she had used a control group. E) This was a legitimate sample drawn from her readers and of sufficient size to allow the conclusion that most of her readers who are parents would have second thoughts about having children.

A) The survey is meaningless because of voluntary response bias.

#2B. Based on your answer to part (a), is there reason to doubt the manager's claim that the 3 people were selected at random? Explain. Nine sales representatives, 6 men and 3 women, at a small company wanted to attend the national convention. There were only enough travel funds to send 3 people. The manager selected 3 people to attend and stated that the people were selected at random. The 3 people selected were women. There were concerns that no men were selected to attend the convention. a) Calculate the probability that randomly selecting 3 people from a group of 6 men and 3 women will result in selecting 3 women. A) Yes, there is reason to doubt the manager's claim, as the probability of RANDOMLY selecting 3 women is low. B) No, because the probability of choosing 3 women is NOT zero, so it IS possible.

A) Yes, there is reason to doubt the manager's claim, as the probability of RANDOMLY selecting 3 women is low.

In a certain community, 20% of cable subscribers also subscribe to the company's broadband service for their Internet connection. You would like to design a simulation to estimate the probability that one of six randomly selected subscribers has the broadband service. Using digits 0 through 9, which of the following assignments would be appropriate to model this situation? A) Assign even digits to broadband subscribers and odd digits to cable-only subscribers. B) Assign 0 and 1 to broadband subscribers and 2,3,4,5,6,7,8, and 9 to cable-only subscribers. C) Assign 0,1, and 2 to broadband subscribers and 3,4,5,6,7,8, and 9 to cable-only subscribers. D) Assign 1,2,3,4,5, and 6 to broadband subscribers and 7,8,9, and 0 to cable-only subscribers. E) Assign 0,1, and 2 to broadband subscribers; 3,4,5, and 6 to cable-only subscribers; and ignore digits 7,8, and 9.

B) Assign 0 and 1 to broadband subscribers and 2,3,4,5,6,7,8, and 9 to cable-only subscribers.

A psychologist from Austin, Texas interested in sleep's effect on the ability to learn randomly selects high school students from the area's local high schools. Half the students are randomly selected to sleep between 7 and 8 hours a night while the remaining half sleep as they normally would. At the end of the study, those students who got between 7 and 8 hours of sleep a night scored significantly higher on tests over the curriculum studied at their school. From this the psychologist can conclude A) 2 sample t-test B) matched pairs t-test C) 2 proportion z-test D) linear regression t-test E) chi-squared test for homogeneity for slope

B) matched pairs t-test

A newlywed couple is trying to choose one of two neighborhood supermarkets for their grocery shopping. They decide to randomly select 20 items, check their price at each store, then conduct a test to determine if, on average, one store is significantly less expensive than the other. What test should they conduct? A) Two-proportion z-test B) Two-sample t-test C) Matched pairs t-test D) t-test for regression slope E) χ2 goodness of fit test

C) Matched pairs t-test

Which of the following is a true statement about experimental design? A) Replication is a key component in experimental design. Thus, an experiment needs to be conducted on repeated samples before generalizing results. B) Control is a key component of experimental design. Thus, a control group that receives a placebo is a requirement for experimentation. C) Randomization is a key component in experimental design. Randomization is used to reduce bias. D) Blocking eliminates the effects of all lurking variables. E) The placebo effect is a concern for all experiments.

C) Randomization is a key component in experimental design. Randomization is used to reduce bias.

Respondents to a randomly distributed questionnaire answered the question, "Do you agree that nuclear weapons should never be used because they are immoral?" The study that uses the results of this questionnaire will most likely suffer from which type(s) of bias? A) undercoverage B) voluntary response C) response D) nonresponse E) all of the above

C) response

An experimenter believes that two new exercise programs are more effective than any current exercise routines and wishes to compare the effectiveness of these two new exercise programs on physical fitness. The experimenter is trying to determine whether or not a control group, which follows neither of these new programs but continues with current exercise routines, would be beneficial. Which of the following can be said about the addition of a control group? A) A control group would eliminate the placebo effect. B) A control group would eliminate the need for blinding in the study. C) A control group would allow the experimenter to determine which of the two exercise programs improves physical fitness the most. D) A control group would allow the experimenter to determine if either of the exercise programs is more effective than current programs for physical fitness. E) There would be no added benefit to having a control group.

D) A control group would allow the experimenter to determine if either of the exercise programs is more effective than current programs for physical fitness.

A study is made to determine whether studying Latin helps students achieve higher scores on the verbal section of the SAT exam. In comparing records of 200 students, half of whom have taken at least 1 year of Latin, it is noted that the average SAT verbal score is higher for those 100 students who have taken Latin than for those who have not. Based on this study, guidance counselors begin to recommend Latin for students who want to do well on the SAT exam. Which of the following are true statements? I. While this study indicates relation, it does not prove causation. II. There could well be a confounding variable responsible for the seeming relationship. III. Self-selection here makes drawing the counselors' conclusion difficult. A) I and II B) I and III C) II and III D) I,II, and III E) None of these

D) I,II, and III

A drug company wishes to test a new drug. A researcher assembles a group of volunteers and randomly assigns them to one of two groups---one to take the drug and one to take a placebo. In addition, the company wants the experiment to be double-blind. What is the meaning of double-blind in this situation? A) The volunteers in both groups are blindfolded when they take the drug or placebo. B) The volunteers in both groups do not know whether they are taking the drug or the placebo. C) Neither the volunteers nor the drug company executives know which volunteers are taking the drug and which are taking the placebo. D) Neither the volunteers nor the evaluator know which volunteers are taking the drug and which are taking the placebo. E) As long as the subjects are randomly assigned to the two groups, there is no need to make the experiment double-blind.

D) Neither the volunteers nor the evaluator know which volunteers are taking the drug and which are taking the placebo.

A group of students has 60 houseflies in a large container and needs to assign 20 to each of the three groups labeled A, B, and C for an experiment. They can capture the flies one at a time when the flies enter a side chamber in the container that is baited with food. Which of the following methods will be most likely to result in three comparable groups of 20 houseflies each? A) Label the first 20 flies caught as Group A, the second 20 caught as group B, and the third 20 caught as group C. B) Write the letters A, B, and C on separate slips of paper. Randomly pick one of the slips of paper and assign the first 20 flies caught to that group. Pick another slip and assign the next 20 flies caught to that group. Assign the remaining flies to the remaining group. C) When each fly is caught, roll a die. If the die shows an even number, the fly is labeled A. If the die shows an odd number, the fly is labeled B. When 20 flies have been labeled A and 20 have been labeled B, the remaining flies are then labeled C. D) Place each fly in its own numbered container (numbered from 1 to 60) in the order that it was caught. Write the numbers from 1 to 60 on slips of paper, put the slips in a jar, and mix them well. Pick 20 numbers out of the jar. Assign the flies in the containers with those numbers to group A. Pick 20 more numbers and assign the flies in the containers with those numbers to group B. Assign the remaining 20 flies to group C. E) When each fly is caught, roll a die. If the die shows a 1 or 2, the fly is labeled A. If the die shows a 3 or 4, the fly is labeled B. If the die shows a 5 or 6, the fly is labeled C. Repeat this process for all 60 flies.

D) Place each fly in its own numbered container (numbered from 1 to 60) in the order that it was caught. Write the numbers from 1 to 60 on slips of paper, put the slips in a jar, and mix them well. Pick 20 numbers out of the jar. Assign the flies in the containers with those numbers to group A. Pick 20 more numbers and assign the flies in the containers with those numbers to group B. Assign the remaining 20 flies to group C.

A cause-and-effect relationship between two variables can best be determined from which of the following? A) A survey conducted using a simple random sample of individuals. B) A survey conducted using a stratified random sample of individuals. C) When the two variables have a correlation coefficient near 1 or ─1. D) An observational study where the observational units are chosen randomly. E) A controlled experiment where the observational units are assigned randomly to treatments.

E) A controlled experiment where the observational units are assigned randomly to treatments.

Which of the following is NOT a characteristic of stratified random sampling? A) Random sampling is part of the sampling procedure. B) The population is divided into groups of units that are similar on some characteristic. C) The strata are based on facts known before the sample is selected. D) Each individual unit in the population belongs to one and only one of the strata. E) Every possible subset of the population, of the desired sample size, has an equal chance of being selected.

E) Every possible subset of the population, of the desired sample size, has an equal chance of being selected.

A volunteer for a mayoral candidate's campaign periodically conducts polls to estimate the proportion of people in the city who are planning to vote for this candidate in the upcoming election. Two weeks before the election, the volunteer plans to double the sample size in the polls. The main purpose of this is to A) reduce nonresponse bias B) reduce the effects of confounding variables C) reduce bias due to the interviewer effect D) decrease the variability in the population E) decrease the standard deviation of the sampling distribution of the sample proportion

E) decrease the standard deviation of the sampling distribution of the sample proportion

#1A: What is the OFF CAMPUS proportion? (For this type of problem, to get full credit you must show both the ratio AND the decimal. If you forget the ratio, then you won't get credit.) A) 0.3731 B) 0.1791 C) 0.7273 D) 0.5152 E) 0.2121 F) 0.5522

F) 0.5522

What are the null and alternative hypotheses? Ho: The distribution of proportions of age-group and whether an adult consumes 5 or more veggies/fruits per day in the U.S. are THE SAME. Ha: The distribution of proportions of age-group and whether an adult consumes 5 or more veggies/fruits per day in the U.S. are DIFFERENT. Ho: Age-group and whether an adult consumes 5 or more servings of veggies/fruits per day in the U.S. are DEPENDENT. Ha: Age-group and whether an adult consumes 5 or more servings of veggies/fruits per day in the U.S. are INDEPENDENT. Ho: There is NO association between age-group and whether an adult consumes 5 or more servings of veggies/fruits per day in the U.S. Ha: There IS an association between age-group and whether an adult consumes 5 or more servings of veggies/fruits per day in the U.S.

Ho: There is NO association between age-group and whether an adult consumes 5 or more servings of veggies/fruits per day in the U.S. Ha: There IS an association between age-group and whether an adult consumes 5 or more servings of veggies/fruits per day in the U.S.

#2C. Choose ALL that apply. c) An alternative to calculating the exact probability is to conduct a simulation to estimate the probability proposed simulation process is described below. Each trial in the simulation consists of rolling three fair, nine-sided dice, one die for each of the convention attendees. For each die, rolling a 1,2,3,4,5, or 6 represents selecting a man; rolling a 7,8, or 9 represents selecting a woman. After 1,000 trials, the number of times, the dice indicate selecting 3 women is recorded. Does the proposed process correctly simulate the random selection of 3 women from a group of 9 people consisting of 6 men and 3 women? Explain why or why not. No, in reality, we are selecting people WITHOUT replacement. The probability of selecting a woman CHANGES from one selection to the next. On the dice, the probability of "selecting a woman" remains constant at 3/9 (or one-third) on all three selections. (This would be sampling with replacement.) P(all 3 dice land 7, 8, or 9) = (3/9)*(3/9)*(3/9) = 1/27 or about 0.037, which is different than 0.0119.

No, in reality, we are selecting people WITHOUT replacement. The probability of selecting a woman CHANGES from one selection to the next. On the dice, the probability of "selecting a woman" remains constant at 3/9 (or one-third) on all three selections. (This would be sampling with replacement.) P(all 3 dice land 7, 8, or 9) = (3/9)*(3/9)*(3/9) = 1/27 or about 0.037, which is different than 0.0119.

What is the probability? An important method for controlling the spread of the h6n2 influenza (bird flu) virus in chickens is having a procedure to determine whether chickens are infected with the virus. it is common to apply a procedure, called an elisa test, to measure the concentration of anti-bird flu antibodies in a blood sample taken from a chicken. if the elisa test reveals a high-enough concentration of antibodies, the chicken is said to test positive, and it is classified as infected with the virus. otherwise, the chicken is said to test negative, and it is classified as not infected. however, the elisa test is a complex procedure that is not always accurate. one type of mistake, a false positive result, occurs when the elisa test gives a positive result for a chicken that is not infected with the virus. a second type of mistake, a false negative result, occurs when the elisa test gives a negative result for an infected chicken. The ELISA test is known to have a probability of 0.05 of producing a false positive result and probability 0.10 of producing a false negative result for a single chicken. b) Veterinarians have developed a procedure where they will randomly select 10 chickens from the large flock described in part (a). The ELISA test is performed on a blood sample from each of the 10 chicken, and if at least 3 out of the 10 chickens have positive ELISA test results, then the veterinarians will conclude that the H6N2 virus is present in the flock. Based on your answer to part (a), what is the probability that the veterinarians will conclude that the H6N2 virus is present in this flock? a) 0.3831 b) 0.2112 c) 0.9462 d) 0.1213

a) 0.3831

WHAT IS THE MEAN? In the 4x100 medley relay event, four swimmers swim 100 yards, each using a different stroke. A college team preparing for the conference championship looks at the times their swimmers have posted and creates a model based on the following assumptions:• The swimmers' performances are independent.• Each swimmer's times follow a Normal model.• The means and standard deviations of the times (in seconds) are shown;Swimmer Mean Standard deviation Backstroke 50.72 0.24Breaststroke 55.51 0.22Butterfly 49.43 0.25Freestyle 44.91 0.21 a) 200.57 b) 110.44 c) 255.12 d) 106.99

a) 200.57

WHAT IS THE MEAN? A local gourmet donut stand sells a plethora of delicious specialty donuts to folks in downtown Austin. Customers can choose to add extra toppings (such as fruits, nuts, candy, chocolate syrup, etc.) for an additional charge. A business associate has determined that the following probability model defines the amount of money that one customer might spend at their donut stand. X ($ spent) $4.50 $5.50 $6.50 $7.50 $8.00 (the max) P(x) 0.13 0.45 0.27 0.09 0.06 a) What are the mean (a.k.a., expected value) and the standard deviation for the amount of money spent by a customer at this donut stand? a) 5.97 b) 6.57 c) 1.22 d) 9.82

a) 5.97

How would you draw the normal model? b) The team's best time so far this season is 3:19:48 (= 199.48 seconds). What is the probability that the team will beat its own best time at the conference championship? a) Normal Model - option 1 H(200.57, 0.461) b) Normal Model - option 2 H(200.57, 0.461)

a) Normal Model - option 1 H(200.57, 0.461)

#3A. What is the probability? Schools in a certain state receive funding based on the number of students who attend the school. To determine the number of students who attend a school, one school day is selected at random and the number of students in attendance that day is counted and used for funding purposes. The daily number of absences at High School A in the state is approximately normally distributed with mean of 120 students and standard deviation of 10.5 students. (a) If more than 140 students are absent on the day the attendance count is taken for funding purposes, the school will lose some of its state funding in the subsequent year. Approximately what is the probability that High School A will lose some state funding? a) 0.972 b) 0.0287

b) 0.0287

For flights from a particular airport in January, there is a 30 percent chance of a flight being delayed because of icy weather. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem. If one flight is selected at random from the airport in January, what is the probability that the flight selected will have at least one of the two types of delays? HINT: DRAW A TREE DIAGRAM. a) 0.065 b) 0.335 c) 0.350 d) 0.450 e) 0.665

b) 0.335

An advertising agency in a large city is conducting a survey of adults to investigate whether there is an association between highest level of educational achievement and primary source for news. The company takes a random sample of 2500 adults in the city. The results are shown in the table below. a) If an adult is selected at random from this sample, what is the probability that the selected adult is a college graduate or obtains news primarily from the internet? a) 0.553 b) 0.4540 c) 0.5311 d) 0.2993

b) 0.4540

WHAT IS THE STANDARD DEVIATION? In the 4x100 medley relay event, four swimmers swim 100 yards, each using a different stroke. A college team preparing for the conference championship looks at the times their swimmers have posted and creates a model based on the following assumptions:• The swimmers' performances are independent.• Each swimmer's times follow a Normal model.• The means and standard deviations of the times (in seconds) are shown;Swimmer Mean Standard deviation Backstroke 50.72 0.24Breaststroke 55.51 0.22Butterfly 49.43 0.25Freestyle 44.91 0.21 a) 0.511 b) 0.461 c) 0.133

b) 0.461

WHAT IS THE STANDARD DEVIATION? A local gourmet donut stand sells a plethora of delicious specialty donuts to folks in downtown Austin. Customers can choose to add extra toppings (such as fruits, nuts, candy, chocolate syrup, etc.) for an additional charge. A business associate has determined that the following probability model defines the amount of money that one customer might spend at their donut stand. X ($ spent) $4.50 $5.50 $6.50 $7.50 $8.00 (the max) P(x) 0.13 0.45 0.27 0.09 0.06 a) What are the mean (a.k.a., expected value) and the standard deviation for the amount of money spent by a customer at this donut stand? a) 0.223 b) 0.956 c) 0.184 d) 0.334

b) 0.956

Name the inference test A large pet store buys the identical species of adult tropical fish from two different suppliers—Buy-Rite Pets and Fish Friends. Several of the managers at the pet store suspect that the lengths of the fish from Fish Friends are consistently greater than the lengths of the fish from Buy-Rite Pets. Random samples of 8 adult fish of the species from Buy-Rite Pets and 10 adult fish of the same species from Fish Friends were selected and the lengths of the fish, in inches, were recorded, as shown in the table below. Length of Fish Mean Standard Deviation Buy-Rite Pets 3.4, 2.7, 3.3, 4.1, 3.5, 3.4, 3.0, 3.8 3.40 0.434 Fish Friends 3.3, 2.9, 4.2, 3.1, 4.2, 4.0, 3.4, 3.2, 3.7, 2.6 3.46 0.550 Does the data provide convincing evidence that the mean length of the adult fish of the species from Fish Friends is greater than the mean length of the adult fish of the same species from Buy-Rite Pets? a) Matched Pairs z-test b) 2 sample t-test c) Matched Pairs t-test d) 2 proportion t-test e) 2 proportion z-test f) 2 sample z-test

b) 2 sample t-test

CALCULATE the t-score, probability, and write the degrees of freedom a) If the inference problem were a 2-sample t-test... t=4.438524813 p=1.695548588 df=17.46587527 b) If the inference problem were a matched pairs t-test... t=3.956835797 p=0.0016600731 df=9

b) If the inference problem were a matched pairs t-test... t=3.956835797 p=0.0016600731 df=9

What are the null and alternative hypotheses? a) If the inference was a matched pairs t-test... H0: Md = 0 Ha: Md < 0 b) If the inference was a 2-sample t-test... H0: Mb - Mf = 0 Ha: Mb - Mf < 0 OR H0: Mb = Mf Ha: Mb < Mf

b) If the inference was a 2-sample t-test... H0: Mb - Mf = 0 Ha: Mb - Mf < 0 OR H0: Mb = Mf Ha: Mb < Mf

CALCULATE the t-score, probability, and write the degrees of freedom a) If the inference was a matched pairs t-test... t=-1.645392681 p=0.0671489329 df=9 b) If the inference was a 2-sample t-test... t=-0.258586833 p=0.3996255543 df=15.99999332

b) If the inference was a 2-sample t-test... t=-0.258586833 p=0.3996255543 df=15.99999332

For test of independence, you need to show that P(A) equals (or doesn't equal) P(A|B). If they are EQUAL, than the events ARE independent. If they are NOT equal, then the events are DEPENDENT (or not independent). An advertising agency in a large city is conducting a survey of adults to investigate whether there is an association between highest level of educational achievement and primary source for news. The company takes a random sample of 2500 adults in the city. The results are shown in the table below. c) When selecting an adult at random from the sample of 2500 adults, are the events "is a college graduate" and obtains news primarily from the internet" independent? Justify your answer. a) Yes, they are independent. b) No, they are dependent.

b) No, they are dependent.

What is the probability statement? b) The team's best time so far this season is 3:19:48 (= 199.48 seconds). What is the probability that the team will beat its own best time at the conference championship? a) Probability statement - option 1 P(total time > 199.48) = P(z > 2.364) b) Probability statement - option 2 P(total time < 199.48) = P(z < -2.364)

b) Probability statement - option 2 P(total time < 199.48) = P(z < -2.364)

#3A. How would you draw the normal model? Schools in a certain state receive funding based on the number of students who attend the school. To determine the number of students who attend a school, one school day is selected at random and the number of students in attendance that day is counted and used for funding purposes. The daily number of absences at High School A in the state is approximately normally distributed with mean of 120 students and standard deviation of 10.5 students. (a) If more than 140 students are absent on the day the attendance count is taken for funding purposes, the school will lose some of its state funding in the subsequent year. Approximately what is the probability that High School A will lose some state funding? a) shade to the LEFT b) shade to the RIGHT

b) shade to the RIGHT

A growing number of employers are trying to hold down the costs that they pay for medical insurance for their employees. As part of this effort, many medical insurance companies are now requiring clients to use generic brand medicines when filling prescriptions. An independent consumer advocacy group wanted to estimate the difference, in milligrams, in the mean amount of active ingredient between a certain "name" brand drug and its generic counterpart. Pharmacies may store drugs under different conditions. Therefore, the consumer group randomly selected ten different pharmacies in a large city and filled two prescriptions at each of these pharmacies, one for the "name" brand and the other for the generic brand of the drug. The consumer group's laboratory then tested a randomly selected pill from each prescription to determine the amount of active ingredient in the pill. The results are given in the following table. ACTIVE INGREDIENT (in milligrams) Pharmacy 1 2 3 4 5 6 7 8 9 10 Name brand 245 244 240 250 243 246 246 246 247 250 Generic brand 246240 235 237 243 239 241 238 238 234 Based on these results, does the consumer group have statistical evidence that the mean amount of active ingredient for the name brand of this drug is greater than the mean amount of active ingredient for the generic brand? Explain. a) 2 sample t-test b) 2 proportion t-test c) Matched Pairs t-test d) 2 sample z-test e) Matched Pairs z-test f) 2 proportion z-test

c) Matched Pairs t-test

The probability that a new microwave oven will stop working in less than 2 years is 0.05. The probability that anew microwave oven is damaged during delivery and stops working in less than 2 years is 0.04. The probability that a new microwave oven is damaged during delivery is 0.10. Given that a new microwave oven is damaged during delivery, what is the probability that it stops working in less than 2 years? a) 0.05 b) 0.06 c) 0.10 d) 0.40 e) 0.50

d) 0.40

A police officer is using a radar device to check motorists' speeds. Prior to beginning the speed check, the officer estimates that 40 percent of motorists will be driving more than 5 miles per hour over the speed limit. Assuming that the police officer's estimate is correct, what is the probability that among 4 randomly selected motorists, the officer will find at least 1 motorist driving more than 5 miles per hour over the speed limit? a) 0.0256 b) 0.1296 c) 0.3456 d) 0.8704 e) 0.9

d) 0.8704

A complex electronic device contains three components, A, B, and C. The probabilities of failure for each component in any one year are 0.01, 0.03, and 0.04, respectively. If any one component fails, the device will fail. If the components fail independently of one another, what is the probability that the device will not fail in one year? a) Less than 0.01 b) 0.078 c) 0.080 d) 0.922 e) Greater than 0.99

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