Math 210 - Exam 4 - Sample Exam

1) What is the p-value for testing H1: µ < 90 if the test statistic is t=-1.592 and n=8?

A) 0.1554 B) 0.0557 C) 0.0750 D) 0.0777

2) The owner of a football team claims that the mean attendance at games is over 83,400, and he is therefore justified in moving the team to a city with a larger stadium. Identify the type II error for the test.

A) Fail to reject the claim that the mean attendance is greater than 83,400, when it is actually less than or equal to 83,400.

B) Reject the claim that the mean attendance is equal to 83,400 when it is actually 83,400.

C) Fail to reject the claim that the mean attendance is at most 83,400, when it is actually greater than 83,400.

D) Fail to reject the claim that the mean attendance is at least 83,400, when it is actually less than 83,400.

*3) Use the Minitab output below to obtain a 90% confidence interval for*
*the population proportion, p.*

**Test for One Proportion**
Test of p = 0.47 vs p < 0.47

X N Sample p Z-Value P-Value

? 315 0.448 -0.796 0.213

A)0.375 < p < 0.520 B)0.393 < p < 0.503 C)0.402 < p < 0.494 D)0.382 < p < 0.513

4) Based on 500 randomly selected lawsuits, 349 were dropped or dismissed. What should H1 be to test the claim that the majority of lawsuits are dropped or dismissed?

A) H1: p 0.698 B) H1: p > 0.698 C) H1: p > 0.5 D) H1: p 0.5

5) It is claimed that the proportion of unlisted telephone numbers in Nevada is less than 60% (H1: p < 0.6). Which of the following is a Type II error?

A) Concluding the proportion of unlisted telephone numbers is at least 0.6 when in fact it is at least 0.6.

B) Concluding the proportion of unlisted telephone numbers is less than 0.6 when in fact it is less than 0.6.

C) Concluding the proportion of unlisted telephone numbers is at least 0.6 when in fact it is less than 0.6.

D) Concluding the proportion of unlisted telephone numbers is less than 0.6 when in fact it is at least 0.6.

6) Based on a sample of 10 observations, the sample mean is 10.2 and a 90% confidence interval for the mean is 7.9 < µ < 12.5. If we test H1: µ 7 at the 0.1 significance level, what is the conclusion?

A) Fail to reject H0 since 7 is not in the interval.

B) Reject H0 since 7 is not in the interval.

C) Fail to reject H0 since 10.2 is in the interval.

D) Reject H0 since 10.2 is in the interval.

7) In a sample of 47 adults selected randomly from one town, it is found that 9 of them have been exposed to a particular strain of the flu. Find the test statistic for a test of the claim that the proportion of all adults in the town that have been exposed to this strain of the flu is 8%.

A) 2.759 B) 0.0024 C) 0.0048 D) 2.817

*8) For the Minitab output below, determine the test statistic.*

**One-Sample T**

Test of mu = 450 vs mu not = 450

N Mean StDev SE Mean T P 23 440.67 12.91 2.692 ? ?

9) Carter Motor Company claims that its new sedan, the Libra, will average better than 26 miles per gallon in the city. Determine the alternative hypothesis.

A) H1: µ < 26 B) H1: µ > 26 C) H0: µ < 26 D) H0: µ > 26 10) Suppose you wish to test H1: µ < 40. Given n = 23 and a significance level of = 0.05,

what criterion would be used for rejecting the null hypothesis?

A) Reject H0 if the test statistic is less than -1.714.

B) Reject H0 if the test statistic is less than -1.960.

C) Reject H0 if the test statistic is less than -1.717.

D) Reject H0 if the test statistic is less than -1.645.

11) What is the p-value for testing H1: p 0.2 if the test statistic is z=-1.04?

A) 0.2983 B) 0.1491 C) 0.6621 D) 0.8508

12) A random sample of 106 body temperatures finds that the average body temperature is 98.2 and sample standard deviation is 2.4. What is the p-value needed to test the claim that the mean body temperature is less than 98.6 (H1: µ < 98.6)?

A) 0.011 B) 0.159 C) 0.067 D) 0.045

13) What is the critical value needed to test H1: µ < 50 if n = 22 and = 0.05?

A) -1.721 B) -1.645 C) -2.08 D) -1.96

14) It is claimed that the mean weight of airline passengers with carry-on luggage is at most 195 lbs. What is H1 in order to test this?

A) H1: µ 195 B) H1: µ 195 C) H1: µ > 195 D) H1: µ < 195 15) Suppose that a hypothesis test results in a p-value of 0.0698. For which of the following

significance levels will we reject the null hypothesis?

A) 0.01 B) 0.1 C) 0.005 D) 0.05

16) A random sample of shoppers at a grocery store is taken and the amount spent by each is recorded. The manager of the store wants to test the claim that the mean amount spent by shoppers is less than $30 (H1: µ < 30). The Minitab output below shows the result of the test. At the 0.1 significance level, what conclusion can be drawn?

**One-Sample T**

Test of mu = 30 vs mu < 30

N Mean StDev SE Mean T P 17 28.13 12.18 2.954 -0.633 0.2678

A) Reject H0 since 28.13 < 30. B) Reject H0 since 0.2678 > 0.1.

C) Fail to reject H0 since 28.13 < 30. D) Fail to reject H0 since 0.2678 > 0.1.

17) A research institute claims the mean length of dreams is more than 10

minutes (H1 : µ > 10). A random sample of 30 dreams finds that the average

length is 12.2 minutes and standard deviation is 5.2 minutes. Find the p-value for testing the claim.

A) 0.0204 B) 0.0102 C) 0.0138 D) 0.0276

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, 32% of them plan to go into general practice. Find the P-value for a test of the school's claim.

A) 0.137 B) 0.3461 C) 0.1635 D) 0.3078

**19) Which of the following is a valid example of H0 and H1?**

A) H0 : p 0.3 vs. H1 : p < 0.3 B) H0 : µ = 50 vs. H1 : µ < 50 C) H0 : 3 vs. H1 : < 3 D) H0 : s = 2 vs. H1 : s 2

21) A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 1 in a thousand. Identify the type I error for the test.

A) Fail to reject the claim that the proportion of Americans that have seen a UFO is at least 1 in a thousand when that proportion is actually greater than 1 in a thousand.

B) Reject the claim that the proportion of Americans that have seen a UFO is at least 1 in a thousand when that proportion is actually less than 1 in a thousand.

C) Fail to reject the claim that the proportion of Americans that have seen a UFO is at least 1 in a thousand when that proportion is actually less than 1 in a thousand.

D) Reject the claim that the proportion of Americans that have seen a UFO is at least 1 in a thousand when that proportion is actually at least 1 in a thousand.

22) A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 2 in every ten thousand. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

A) There is sufficient evidence to support the claim that the true proportion is greater than 2 in ten thousand.

B) There is not sufficient evidence to support the claim that the true proportion is less than 2 in ten thousand.

C) There is not sufficient evidence to support the claim that the true proportion is greater than 2 in ten thousand.

D) There is sufficient evidence to support the claim that the true proportion is less than 2 in ten thousand.

23) A computer repairer believes that the mean cost for repairing a damaged computer is more than $95 (H1 : µ > 95). To test this claim, a sample of n = 18 randomly selected computers needing repair is obtained. The sample mean cost is $100 with sample standard deviation $12. What’s the test statistic for testing this claim?

A) 2.912 B) 1.767 C) 1.387 D) 2.474

24) In tests of a computer component, it is found that the mean time between failures is 520 hours. A modification is made which is supposed to increase the time between failures.

Tests on a random sample of 10 modified components resulted in the following times (in hours) between failures.

518 548 561 523 536 499 538 557 528 563

What is the p-value needed to test the claim that the mean time between failures has increased after this modification?

A) 0.0282 B) 0.0141 C) 0.0045 D) 0.0090

25) Find the p-value for testing H1: µ 50 if the test statistic is t=-1.04 and n=15?

A) 0.3160 B) 0.1492 C) 0.2983 D) 0.1580