Exam 3 review

1. You are testing  for a normal population. The 95% confidence interval for the mean is (0.58,0.64)

a) The p-value is greater than 0.05

b) The p-value is less than 0.05

c) The p-value cannot be determined without the sample size.

 

2. An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to use in making potato chips. She intends to compute a 95% confidence interval for p. To do so she selects an SRS of 100 potatoes from the over 2000 potatoes on the truck. Suppose only 4 of the potatoes sampled are found to have major defects. Which of the following assumptions for inference about a proportion, using a confidence interval are violated?

a) The population is at least ten times as large as the sample.

b) n is so large that  and  are ten or more.

c) No violations.

 

3. A type II error is

a) rejecting the null hypothesis when it is true.

b) Failing to reject the null hypothesis when it is false.

c) Incorrectly specifying the null hypothesis.

d) Incorrectly specifying the alternative hypothesis.

 

4. A researcher plans to conduct a test of hypotheses at level of significance 0.01. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest. The probability that the researcher will make a type II error for the particular alternative value of the parameter at which she computed the power is

a) 0.01                         b) 0.10              c) 0.90                         d) Equal to 1-(p-value)

 

5. A random sample of 100 midmorning shoppers at a supermarket revealed that 90 included milk as one of their purchases. Construct a 99% confidence interval for the true proportion who buy milk.

6. We want to estimate, with a maximum error of 0.03, the true proportion of all TV households tuned in to a particular show, and we want 95% confidence in our results. How many TV households must we survey?

7. You find that in a sample of 1762 Americans, 1004 of them believe that government regulation of business does more harm than good. At the .05 significance level, is there enough evidence to reject the claim that 60% of Americans have this view?

a) State the null and alternative hypotheses.

b) Calculate the test statistic. 

c) Calculate the p-value of the test statistic. P = 2(.0051) = .0102

d) Make a statistical conclusion. p < .05 so reject the null hypothesis

e) Interpret your conclusion to someone who knows nothing about statistics.

There is sufficient evidence to reject the claim that 60% believe government regulation does more harm than good.

 

8. True or false:

a) Even with a random sample, a hypothesis test could result in an incorrect decision True

b) A type II error occurs when  is not rejected, but  is false. True

 

9. Scores on the Math Scholastic Aptitude Test (MSAT) are normally distributed with mean 500 and standard deviation 100.

If a random sample of 50 scores is obtained, what is the probability that the average score will be between 480 and 540?

10. Out of a SRS of 100 students at a university, 82 stated that they were nonsmokers.

a) Based on this, construct a 99% confidence interval estimate of the proportion of all students at the university who are nonsmokers.

b) Interpret your confidence interval.

We can be 99% confident the true proportion of non-smokers is between .72 and .92

c) What sample size would need to be used in order to reduce the margin of error in this problem to 0.05?

 

11. A travel agent wishes to estimate, with 98% confidence, the proportion of vacationers who use an online service or the Internet to make reservations for lodging. Your estimate must have a maximum margin of error of 0.04. A prior study found 0.10 of the respondents said they used an online service or the Internet to make reservations for lodging. How large an SRS is required?

12. Suppose 40% of the adult residents in North Dakota favor the death penalty. In an SRS of 100 North Dakota adult residents, what is the probability that more than 50% of them favor the death penalty?

13. An attorney claims that more than 25% of all lawyers advertise. A sample of 200 lawyers in a certain city showed that 63 had used some form of advertising. Using a level of significance of 0.05, is there evidence to support the attorney’s claim?

a) State the null and alternative hypotheses.

b) Calculate the test statistic.

c) Calculate the p-value of the test statistic. P = .0170

d) Make a statistical conclusion. p < .05 so reject the null hypothesis

e) Interpret your conclusion to someone who knows nothing about statistics.

There is sufficient evidence to show that more than 25% of all lawyers advertise.

 

14. Many Americans think it doesn’t matter which political party controls Congress. In an Associated Press article, it was reported that 442 individuals in a sample of 1100 U.S. adults said it wouldn’t make much difference which party is in power.

a) Construct a 95% confidence interval estimate of the proportion of all U.S. adults who believe that it wouldn’t make much difference which party is in power.

b) Interpret your confidence interval.

We can be 95% confident that the true proportion who feel it wouldn’t matter which party is in power is between .373 and .431

c) Based on your interval in (a), is it plausible that 50% of U.S. adults feel that it makes no difference which party is in control? Explain your reasoning.

.5  is not in the 95% confidence interval, so reject the hypothesis that p = .5: it is not plausible that 50% feel this way

 

15. A type II error is made when:

a) We fail to reject the null hypothesis when it is true.

b) We fail to reject the null hypothesis when it is false.

c) The null hypothesis is rejected when it is true.

d) The null hypothesis is rejected when it is false.

 

16.   In testing hypotheses, which of the following would be strong evidence against the null hypothesis?

a) Obtaining data with a small P-value

b) Obtaining data with a large P-value

c) Obtaining a large b probability

d) Obtaining a large a probability

 

17. If a is the probability of type I error and b is the probability of a type II error, which of the following statements is correct?

a) If a is small, then b is small too

b) If a is large, then b is large too

c) If a decreases, then b increases

d) Both (a) and (b)

e) None of the above

 

18.A research biologist has carried out an experiment on a random sample of 15 experimental plots in a field. Following the collection of data, a test of significance was conducted under appropriate null and alternative hypotheses and the P-value was determined to be approximately .03. This indicates that:

a) There is some evidence to indicate that the null hypothesis is incorrect.

b) If this experiment were repeated many times, 3 per cent of the time we would get this same result.

c) This result is statistically significant at the .01 level.

d) The probability of being wrong in this situation is only .03.

 

19. During a pre-dive check, a scuba diver discovers a minor problem - a warning light indicates that the air gauge may be broken. If the diver decides to check the air level manually, it will delay the dive by 45 minutes. If the diver decides to ignore the warning, he may run out of air during his dive. The null hypothesis in this situation is: assume that the warning can be ignored. What would be a type I error?

a) Decide to ignore the warning when there is in fact enough air.
b) Decide to check the air level manually when there is in fact not enough air.

c) Decide to check the air level manually when there is in fact enough air.
d) Decide to ignore the warning when there is in fact not enough air.
e) Going scuba diving in the first place.