Exam 2 Stats1200

The t statistic for a test of H0:μ=15 HA:μ<15 based on n = 10 observations has the value t =-2.15. (a) What are the degrees of freedom for this statistic? (b) Using the appropriate table in your formula packet, bound the p-value as closely as possible: ______<p-value<___________

(a) 9 (b) 0.022 < p < 0.038

In a carnival game, a player spins a wheel that stops with the pointer on one (and only one) of three colors. The likelihood of the pointer landing on each color is as follows: 63 percent BLUE, 23 percent RED, and 14 percent GREEN. (b) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on RED. What is the probability that we will spin the wheel at least three times?

(1-0.23)^2

In a carnival game, a player spins a wheel that stops with the pointer on one (and only one) of three colors. The likelihood of the pointer landing on each color is as follows: 63 percent BLUE, 23 percent RED, and 14 percent GREEN. (a) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on BLUE. What is the probability that we will spin the wheel exactly three times?

(1-0.63)^2 *0.63

1. A consumer believes that a certain potato chip maker is putting fewer chips in their regular bags of chips than the advertised amount of 12 ounces. In order to test the null hypothesis that the average chip weight is 12 ounces per bag vs. the alternative hypothesis that the average chip weight is less than 12 ounces per bag, a random sample of 50 bags were selected. The resulting data produced a p - value of 0.072. (a) At a 5% level of significance, should the null hypothesis be rejected? (Type: Yes or No): (b) At a 10% level of significance, should the null hypothesis be rejected? (Type: Yes or No): 2. In a statistical test of hypotheses, saying that ''the evidence is statistically significant at the .05 level'' means A. the p-value is at least .05. B. α is more than .25. C. α=.10. D. the p-value is less than .05.

(a) NO (b) YES 2. D. the p-value is less than .05.

The t statistic for a test of H0:μ=34 HA:μ>34 based on n = 17 observations has the value t = 2.15. (a) What are the degrees of freedom for this statistic? (b) Using the appropriate table in your formula packet, bound the p-value as closely as possible: _____<p-value<______

(a 16 (b) 0.017< p < 0.031

For each situation, state the null and alternative hypotheses: (Type "mu" for the symbol μ, e.g. mu > 1 for the mean is greater than 1, mu <1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1. (a) The diameter of a spindle in a small motor is supposed to be 4.9 millimeters (mm) with a standard deviation of 0.12 mm. If the spindle is either too small or too large, the motor will not work properly. The manufacturer measures the diameter in a sample of 51 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 4.82 mm. H0: Ha: (b) Harry thinks that prices in Caldwell, Idaho, are lower than the rest of the country. He reads that the nationwide average price of a certain brand of laundry detergent is $15.75 with standard deviation $1.25. He takes a sample from 33 local Caldwell stores and finds the average price for this same brand of detergent is $13.19. H0: Ha:

(a) H0: mu = 4.9 Ha: mu not = 4.9 (b) H0: mu = 15.75 Ha: mu < 15.75

An article published in the Washington Post claims that 45 percent of all Americans have brown eyes. A random sample of n=82 college students found 30 who had brown eyes. Consider testing H0: p= .45 Ha: p≠ .45 (a) The test statistic is z= (b) P-value =

(a) -1.533 (b) 0.12

(a) Find the P - value for the test statistic z=−1.41 for the following null and alternative hypotheses: H0: The population mean is 50. Ha: The population mean is less than 50. The P - value is (b) Find the P - value for the test statistic z=−1.41 for the following null and alternative hypotheses: H0: The population mean is 50. Ha: The population mean is not equal to 50. The P - value is

(a) 0.0793 (b) 0.16

Choose a student in grades 9 to 12 at random and ask if he or she is studying a language other than English. X= LANGUAGE, SPANISH, FRENCH, GERMAN, ALL OTHERS, NONE Y= PROBABILITY, 0.2, 0.06, 0.04, 0.04, 0.66 (a) What is the probability that a randomly chosen student is, in fact, studying a language other than English? (b) What is the probability that a randomly chosen student is studying French, German, or Spanish? (c) What is the probability that a randomly chosen student is studying a language besides English, but not German?

(a) 0.34 (b) 0.3 (c) 0.3

A random sample of 80 Mizzou students showed that 40 had driven a car during the day before the survey was conducted. Suppose that we are interested in forming a 99 percent confidence interval for the proportion of all Mizzou students who drove a car the day before the survey was conducted. (a) The estimate is: (b) The standard error is: (c) The multiplier is:

(a) 0.5 (b)0.56 (c)2.576

EVENT, attend a 4-yr college, attend a junior college, attend a tech school, train as an apprentice, no formal training after HS PROBABILITY, 0.2, 0.2, 0.1, 0.1, 0.4 At a certain high school, if a student is selected at random and asked what they plan to do after graduating, the probability distribution for their response is given above. Determine the following: (a) P(Receive some sort of formal training after high school)= (b) P(Receive training after high school but not at a college)= (c) P(Do not attend a 4-year college) =

(a) 0.6 (b) 0.2 (c) 0.8

Nationwide, 70 percent of persons taking a certain professional certification exam pass. Consider, for a samples of 200, the sampling distribution of ^ P (a) the mean of the sampling distribution of (^P) is: (b) the SD of the sampling distribution of (^P) is:

(a) 0.7 (b) 0.0324

A random sample of n=1200 registered voters and found that 620 would vote for the Republican candidate in a state senate race. Let p represent the proportion of registered voters who would vote for the Republican candidate. Consider testing H0: p= .50 Ha: p > .50 (a)The test statistic is z = (b) Regardless of what you actually computed, suppose your answer to part (a) was z= 1.28, using this z, p value =

(a) 1.1547 (b) 0.1

A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. A random sample of 36 stores this year shows mean sales of 84 units of a small appliance with a standard deviation of 15 units. During the same point in time last year, a random sample of 49 stores had mean sales of 66 units with standard deviation 17 units. It is of interest to construct a 95 percent confidence interval for the difference in population means μ1−μ2, where μ1 is the mean of this year's sales and μ2 is the mean of last year's sales. (a) The estimate is: (b) The Standard error is:

(a) 18 (b)3.485

A measurement is normally distributed with μ=23.5 and σ=6.1 (a) The mean of the sampling distribution of x for samples of size 9 is: (b) The standard deviation of the sampling distribution of x for samples of size 9 is:

(a) 23.5 (b) 2.033

The t statistic for a test of H0:μ=57 HA:μ≠57 based on n = 6 observations has the value t = 1.32. (a) What are the degrees of freedom for this statistic? (b) Using the appropriate table in your formula packet, bound the p-value as closely as possible: ___<p-value<_____

(a) 5 (b) < p <

Jen thinks a certain potato chip maker is putting less product in their personal-sized bags of chips. In the past, these bags contained one ounce of product. Jen conducted a test of H0:μ=1 vs. HA:μ<1. From a random sample of 15 bags of potato chips she calculated a p - value of 0.016 for the sample. (a) At a 5% level of significance, is there evidence that Jen is correct? (Type Yes or No): (b) At a 10% level of significance, is there evidence that she is correct? (Type Yes or No):

(a) YES (b) YES

The hemoglobin count (HC) in grams per 100 milliliters of whole blood is approximately normally distributed with a population mean of 14 for healthy adult women. Suppose a particular female patient has had 19 laboratory blood tests during the past year. The sample readings showed an average HC of 17.53 with a standard deviation of 2.61. Does it appear that the population average HC for this patient is not 14? (a) State the null and alternative hypotheses: (Type "mu" for the symbol μ , e.g. mu > 1 for the mean is greater than 1, mu < 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1) H0: Ha: (b) Find the test statistic, t =

(a) mu = 14 mu not = 14 (b) 5.895

Lois thinks that people living in a rural environment have a healthier lifestyle than other people. She believes the average lifespan in the USA is 77 years. A random sample of 20 obituaries from newspapers from rural towns in Idaho give x¯=80.04 and s=2.26. Does this sample provide evidence that people living in rural Idaho communities live longer than 77 years? (a) State the null and alternative hypotheses: (Type "mu" for the symbol μ, eg. mu >1 for the mean is greater than 1, mu < 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1) H0: Ha: (b) Find the test statistic, t =

(a) mu= 77 mu > 77 (b) 6.015

A recent survey showed that among 100 randomly selected college seniors, 20 plan to attend graduate school and 80 do not. Determine a 99 % confidence interval for the population proportion of college seniors who plan to attend graduate school. 99% CI: ____ to _____

0.096 0.303

A biologist claims that nearly 45 percent of all Americans have brown eyes. A random sample of n=90 Mizzou students found 18 with brown eyes. Give the numerical value of the statistic ^ P ^ P=

0.2

Government data assign a single cause for each death that occurs in the United States. (Thus, in government terminology, causes of death are mutually exclusive.) In a certain city, the data show that the probability is 0.35 that a randomly chosen death was due to cardiovascular (mainly heart) disease, and 0.15 that it was due to cancer. (a) The probability that a death was due either to cardiovascular disease or to cancer is (b) The probability that the death was not due to either of these two causes is

0.35+0.15 0.5

Suppose that, for students who are enrolled in college algebra, 80 percent are freshmen, 41 percent are female, and 29 percent are female and are freshmen. Your answers below should be entered as decimals and rounded to three decimal places. (c) Two students will be independently selected at random. What is the probability that both of the selected students will be female?

0.41^2

Suppose that, for students who are enrolled in college algebra, 80 percent are freshmen, 41 percent are female, and 29 percent are female and are freshmen. Your answers below should be entered as decimals and rounded to three decimal places. (a) One student will be selected at random. What is the probability that the selected student will be a freshman or female (or both)?

0.8+0.41-0.29

In a carnival game, a player spins a wheel that stops with the pointer on one (and only one) of three colors. The likelihood of the pointer landing on each color is as follows: 63 percent BLUE, 23 percent RED, and 14 percent GREEN (c) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on GREEN. What is the probability that we will spin the wheel 2 or fewer times?

1-(1-0.14)^2

Suppose that, for students who are enrolled in college algebra, 80 percent are freshmen, 41 percent are female, and 29 percent are female and are freshmen. Your answers below should be entered as decimals and rounded to three decimal places. (b) One student will be selected at random. What is the probability that the selected student will not be a freshman?

1-0.8

For patients who have been given a diabetes test, blood-glucose readings are approximately normally distributed with mean 128 mg/dl and a standard deviation 10 mg/dl. Suppose that a sample of 4 patients will be selected and the sample mean blood-glucose level will be computed. According to the empirical rule, in 95 percent of samples the SAMPLE MEAN blood-glucose level will be between the lower-bound of ______ and the upper-bound of______

118 138

In a particular municipality, it is believed that 25 percent of homes are not properly insulated. In order to test H0:p=.25 vs. HA:p≠.25(where p is the population proportion of homes that are not properly insulated) a random sample of 300 homes was selected. In the sample, it was found that 102 homes were not properly insulated. If the null hypothesis is true, then the z-score for the sample proportion is:

3.6

The home states of a certain group of people are distributed as follows: 57 percent are from MISSOURI, 23 percent are from KANSAS, and 20 percent are from IOWA. (No one in the group had a home state other than one of these three.) Suppose we randomly select a person from this group. What is the expected value of the number of letters in the selected person's home state?

8* 0.57+6* 0.23+4* 0.2

Match the confidence level with the confidence interval for the population mean. Type the correct letter in each box. 1. x¯± 1.645(s\sqrt of n) 2. x¯± 1.282 ( s\ sqrt of n) 3. x¯± 2.575 (s\ sqrt of n) A. 90% B. 80% C. 99%

A B C

Blood Type O A B AB Probability 0.12, 0.35, 0.12, ? (a) Maria has type B blood. She can safely receive blood transfusions from people with blood types O and B. What is the probability that a randomly selected person will be able to donate blood to Maria? A. 0.24 B. 0.47 C. 0.12 D. NONE

A. 0.24

Blood Type O A B AB Probability 0.12, 0.35, 0.12, ? (c) The probability that a randomly selected person will have type AB blood is A. 0.41 B. 0.12 C. NONE

A. 0.41

(b) In testing hypotheses, which of the following would tend to be evidence in favor of the alternative hypothesis? A. a small p-value B. a large level of significance C. a large p- value D. a small level of significance.

A. a small p-value

(a) If the knowledge that an event A has occurred implies that a second event B cannot occur, then the events A and B are said to be A. Collectively Exhaustive B. Mutually Exclusive C. The sample space D. Independent (b) If event A and event B are as above and event A has probability 0.5 and event B has probability 0.4, then the probability that A or B occurs is

B 0.5 + 0.4

(a) The p- value of a hypothesis test is A. the probability the null hypothesis is true. B. the probability of observing evidence in favor of the alternative hypothesis as strong or stronger than that which was observed if the null hypothesis were true. C. the probability the null hypothesis is false. D. the probability of observing evidence in favor of the null hypothesis as strong or stronger than that which was observed if the alternative hypothesis were true.

B. The proability of obsering evidence in favor of the alternative hypothesis as strong or stronger than that which was observed if the null hypothesis were true.

For students at a large, state university, consider two groups. Group 1: Students who purchased their textbooks for the current semester at the campus bookstore and Group 2: Students who purchased their textbooks for the current semester online. A 99% confidence interval for μ1−μ2, the difference in population mean amounts spent on textbooks, is 30 to 60 dollars. 2. The confidence interval provides no strong evidence to support or refute the claim that, on average, students who purchased their books at the campus bookstore spent __________ dollars more than those who purchased their books online. A. less than 65 B. more than 50 C. at most 70 D. at least 20 E. more than 25 1. The confidence interval would tend to support the claim that, on average, students who purchased their books at the campus bookstore spent __________ dollars more than those who purchased their books online. A. at least 32 B. more than 65 C. less than 20 D. at most 40 E. at least 25

B. more than 50 E. at least 25

Match the confidence level with the confidence interval for μ1−μ2. Type the correct letter in each box. 1. (x1-x2) +- 2.576 sqrt... 2.1.645 3. 1.96 A. 95% B. 90% C. 99%

C B A

Probability is a measure of how likely an event is to occur. Match one of the probabilities that follow with each statement of likelihood given. 1. This event is very likely to occur, but is not certain to occur. 2. This event is very unlikely to happen, but it will occur once in a while in a long sequence of trials. 3. This event is impossible. It will never happen. 4. This event will occur a little less than half the time over a long sequence of trials. A. 0.42 B. 0.01 C. 0.96 D. 0

C B D A

Blood Type O A B AB Probability 0.12, 0.35, 0.12, ? (b) If two people are selected at random, what is the probability that both people selected will have type O blood? A. 0.24 B. 0.12 C. 0.0144 D. NONE

C. 0.0144

(a) A 90% confidence interval for the mean of a population is computed to be 135 to 160. Which one of the following claims would the interval tend to refute? A. The population mean is less than 150. B. The population mean is more than 140. C. The population mean is less than 125. D. The population mean is between 140 and 150. E. The population mean is more than 110. (b) A 95% confidence interval for the mean of a population is computed to be 6 to 14. Which one of the following claims would the interval tend to support? A. The population mean is exactly 9. B. The population mean is more than 17. C. The population mean is more than 7. D. The population mean is less than 15. E. The population mean is between 8 and 10.

C. The population mean is less than 125. D. The population mean is less than 15.

The fill volume of a random sample 31 cans of Coke were found to have a mean of x¯=12.15 with standard deviation of s=0.11. Find the value of the test statistic z for evaluating the null hypothesis μ=12. The test statistic is

Claimed Hypothesis Mean, H0: 12 Sample mean= 12.15 SD= 0.11 n= 31 Answer= 7.592

A phone-in poll conducted by a newspaper reported that 68% of those who called in liked ''reality TV.'' (a) The number 68% is a A. Parameter B. Sample C. Population D. Statistic (b) The unknown true percentage of American citizens who like "reality TV" is a A. Statistic B. Population C. Sample D. Parameter

D. Statistics D. Parameter

(c) The null hypothesis is A. the same thing as the "research hypothesis" B. the probability of observing the data you actually obtained C. a statement that the data are all 0. D. assumed to be true unless substantial evidence to the contrary is presented.

D. assumed to be true unless substantial evidence to the contrary is presented.

Starting salaries of 64 college graduates who have taken a statistics course have a mean of $43,500 with a standard deviation of $6,800. Find an 80% confidence interval for μ. Lower-bound:___ Upper-bound:____

Lower Bound= 42410.3 Upper Bound = 44589.7

A random sample of n=100 observations produced a mean of x¯ =39 with a standard deviation of s=4 (a) Find a 95% confidence interval for μ lower-bound: ____ Upper-bound: ______ (b) Find a 99% CI for μ Lower-bound:____ Upper-bound:____ (c) Find a 90% CI for μ Lower-bound:____ Upper-bound:_____

a) LB=38.216 UB= 39.784 (b) LB= 37.968 UB= 40.032 (c) LB= 38.344 UB= 39.656