STAT251



ANSWER SHEET

1.

H0:

Ha:

α=.01

rejection region:

calculate test statistic:

conclusion:

determine p-value:

2.

H0:

Ha:

α=.025

rejection region:

calculate test statistic:

conclusion:

determine p-value:

3.

H0:

Ha:

α=.05

rejection region:

calculate test statistic:

conclusion:

determine p-value:

4.

H0:

Ha:

α=.05

rejection region:

calculate test statistic:

conclusion:

determine p-value:

5.

6.

H0:

Ha:

α=.01

rejection region:

calculate test statistic:

conclusion:

determine p-value:

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

STAT511 Homework 2

Due Wednesday, Feb. 19

Instructions You are encouraged to use R for this assignment. Please turn in your scratch work with the answer sheet.

1. In a sample of 88 adults selected randomly from one town, it is found that 6 of them have been exposed to a particular strain of the flu. At the 0.01 significance level, test the claim that the proportion of all adults in the town that have been exposed to this strain of the flue differs from the nationwide proportion of .08.

2. The owners of a large real estate agency believe that a slow economy has lowered the selling prices of homes below last year’s average of $102,000. A random sample of the selling prices of 18 homes sold (expressed in thousands of dollars) reported the following figures:

105.0 104.0 81.0 128.0 74.0 111.0 86.9 87.9 87.0

84.0 92.0 92.9 108.0 85.9 115.0 134.0 84.5 91.9

Do the data provide sufficient evidence to conclude that the average selling price of homes sold by this firm has decreased. Use α=.025.

3. One criticism of reading comprehension tests is that while they may measure reading comprehension, they also measure other factors not related to reading comprehension. A reading comprehension (RC) test on a major college entrance exam provides short English prose passages, and the examinees answer a set of multiple-choice items about the passage. To see if particular items measure something other than RC, investigators gave the RC test without the reading passages to a random sample of psychology students. The investigators reasoned that if questions were measuring knowledge or memory rather than just RC, students would answer questions at a higher rate than chance (20%, since there were 5 choices for each question.)

Suppose that on one question, 30 out of 100 examinees answered the question correctly. Is this sufficient evidence that students are using more than just reading comprehension to answer this question? Test the relevant hypothesis using[pic].

4. A manufacturer of gunpowder has developed a new powder that is designed to produce a muzzle velocity equal to 3000 feet per second. Eight shells are loaded with the charge and muzzle velocities measured. The resulting velocities are as follows:

 

3005 2925 2935 2965 2995 3005 2935 2905

 

Do the data provide sufficient evidence to indicate that the average velocity differs from 3000 feet per second? Conduct hypothesis test using α=.05.

 

5. A survey was conducted to estimate μ, the mean salary of middle-level bank executives. A random sample of 15 executives yielded the following yearly salaries (in units of $1000):

 

88 121 75 39 52 102 95 78

69 82 80 84 72 115 106

Find a 98% confidence interval for μ.

6. A massive multistate outbreak of food-borne illness was attributed to Salmonella enteritidis. Epidemiologists determined that the source of the illness was ice cream. The sampled nine production runs from the company that had produced the ice cream to determine the level of Salmonella enteritidis in the ice cream. These levels (MPN/g) are as follows:

.593 .142 .329 .691 .231 .793 .519 .392 .418

Do the data provide sufficient evidence to conclude that the average level of Salmonella enteritidis in the ice cream is greater than .3 MPN/g, a level that is considered to be very dangerous? Use α=.01.

7. When 293 college students are randomly selected and surveyed, it is found that 114 own a car. Construct a 90% confidence interval for the proportion of all college students who own a car.

8. A simple random sample of students is selected, and the students are asked how much time they spent preparing for a test. The times (in hours) are as follows:

1.3 7.2 4.2 12.5 6.6 2.5 5.5 

Based on these results, a confidence interval for the population mean is found to be [pic]. Find the degree of confidence.

9. A hypothesis test will be performed to test the claim that a population proportion is less than 0.70. A sample size of 400 and significance level of 0.05 will be used. If π = 0.64, find the probability of making a type II error, β.

Multiple Choice Questions:

10. A safety officer wants to demonstrate that [pic] = the average speed of cars driven by a school is less than 25 mph. Suppose that a random sample of 14 cars produces a test statistic of (1.70. What is the p-value?

A) P-value = 0.129

B) P-value = 0.003

C) P-value = 0.017

D) P-value = 0.056

11. The owner of a local nightclub has recently surveyed a random sample of n = 25 customers. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Using α=.025, what rejection region should be used?

A) Reject H0 if t [pic] – 1.711.

B) Reject H0 if t [pic] 2.064

C) Reject H0 if t [pic]– 2.064.

D) Reject H0 if t [pic] 1.711.

12. If we are performing a hypothesis test of H0:[pic]= 100 vs. Ha: μ>100, the probability of rejecting H0 if μ=102 will be ________ the probability of rejecting H0 if μ=108.

A) less than

B) greater than

C) equal to

D) not comparable to

13. In the past, the mean running time for a certain type of flashlight battery has been 9.6 hours. The manufacturer has introduced a change in the production method and wants to perform a significance test to determine whether the mean running time has increased as a result. The hypotheses are:

H0: μ = 9.6 hours

Ha: μ > 9.6 hours

Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean running time has increased.

A) Correct Decision

B) Type I Error

C) Type II error

D) Not enough information

14. Which of the following statements are true?

A) When the research hypothesis is [pic], the null hypothesis [pic] should be rejected if [pic] is too far to the right of [pic].

B) When the research hypothesis is [pic], the null hypothesis [pic] should be rejected if [pic] is too far to the left of [pic].

C) When the research hypothesis is [pic], the null hypothesis [pic] should be rejected if [pic] is too far to either side of [pic].

D) All are true.

15. Consider a test of Ho: ( = 50 versus Ha: ( > 50 using a sample of n = 35 and α = .05 . Is the power of the test increased, decreased, or unchanged if the significance level is changed to α = .10 ?

(A) Increased

(B) Decreased

(C) Unchanged

(D) Not enough information to decide

16. The p-value for a one-tailed test for a mean was 0.04. The p-value for the corresponding two-tailed test would be:

A) 0.02

B) 0.04

C) 0.06

D) 0.08

17. A test of H0: ( = 0 versus Ha: (> 0 is conducted on the same population independently by two different researchers. They both use the same sample size and the same value of ( = 0.05. Which of the following will have to be the same for both researchers?

A) The p-value of the test.

B) The power of the test if ( = 6.

C) The value of the test statistic.

D) The decision about whether or not to reject the null hypothesis.

18. A medical school claims that more than 28% of its students plan to go into general practice. It is found that among a random sample of 130 of the school's students, 40% of them plan to go into general practice. Find the p-value.

A) .2415

B) .1635

C) .3058

D) .0011

19. About 90% of the general population are right-handed. A researcher speculates that artists are less likely to be right-handed than the general population. In a random sample of 100 artists, 83 are right-handed. Which of the following best describes the p-value for this situation?

A) The probability that the population proportion of artists who are right-handed is 0.90.

B) The probability that the population proportion of artists who are right-handed is 0.83.

C) The probability the sample proportion would be as small as 0.83, or even smaller, if the population proportion of artists who are right-handed is actually 0.90.

D) The probability that the population proportion of artists who are right-handed is less than 0.90, given that the sample proportion is 0.83.

20. A sample of n=168 students was asked, “Do you believe in love at first sight?” The choices (below) show confidence intervals, in scrambled order, for 90%, 95%, 98%, and 99% confidence intervals for the population proportion who would answer yes. Which choice gives the 95% confidence interval?

A) .56 to .68

B) .52 to .72

C) .53 to .71

D) .55 to .69

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