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Chapter 9: 3.2 (page 577)

The health director of a large company is concerned about the effects of stress on the company’s middle-aged male employees. According to the National Center for Health Statistics, the mean systolic blood pressure for males 35 to 44 years of age is 128. The health director examines the medical records of a random sample of 72 male employees in this age group. The Minitab output below displays the results of a significance test and a confidence interval.

1. Do the results of the significance test allow us to conclude that the mean blood pressure for all the company’s middle-aged male employees differs from the national average? Justify your answer.

2. Interpret the 95% confidence interval in context. Explain how the confidence interval leads to the same conclusion as in Question 1.

Short Answer

Expert verified

Part (a) Test is not significant.

Part (b) Null hypothesis is rejected.

Step by step solution

01

Part (a) Step 1. Interpretation 

The p-value as indicated in the Minitab output is equal to 0.275 which is greater than 0.05. As a result, the test is not significant and there is insufficient evidence to reject the null hypothesis that there is no difference.

02

Part (b) Step 1. Interpretation 

The sample mean and test statistic as indicated in the Minitab output is equal to 129.93 and 1.10 respectively. If the sample means is extended to either side of the test statistic at a 95% confidence interval will still belong to the confidence interval. As a result, it shows there is insufficient evidence to reject the null hypothesis that there is no difference.

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Most popular questions from this chapter

As part of its 2010 census marketing campaign, the U.S. Census Bureau advertised

“10 questions, 10 minutes—that’s all it takes.” On the census form itself, we read, “The

U.S. Census Bureau estimates that, for the average household, this form will take

about 10 minutes to complete, including the time for reviewing the instructions and

answers.” We suspect that the actual time it takes to complete the form may be longer

than advertised.

Sampling shoppers A marketing consultant observes 50 consecutive shoppers at a supermarket, recording how much each shopper spends in the store. Explain why it would not be wise to use these data to carry out a significance test about the mean amount spent by all shoppers at this supermarket.

A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay \(100for the upgrade. For the upgrade to be profitable, the company needs to sell it to more than 20%of their customers. You contact a random sample of 60customers and find that 16 would be willing to pay \)100for the upgrade.

(a) Do the sample data give good evidence that more than 20%of the company’s customers are willing to purchase the upgrade? Carry out an appropriate test at the A=0.05significance level.

(b) Which would be a more serious mistake in this setting—a Type I error or a Type II error? Justify your answer.

(c) Other than increasing the sample size, describe one way to increase the power of the test in (a).

Is your food safe? Do you feel confident or not confident that the food available at most grocery stores is safe to eat? when a gallup poll asked this question, 87%of the sample said they were confident." Callup announced the poll's margin of error for 95%confidence as±3 percentage points. Which of the following sources of error are included in this margin of error? Explain.

(a) Gallup dialed landline telephone numbers at random and so missed all people without landline phones, including people whose only phone is a cell phone.

(b) Some people whose numbers were chosen never answered the phone in several calls or answered but refused to participate in the poll.

(c) There is chance variation in the random selection of telephone numbers.

A 95%confidence interval for a population mean is calculated to be (1.7,3.5). Assume that the conditions for performing inference are met. What conclusion can we draw for a test of role="math" localid="1650275427722" H0:μ=2versus Ha:μ≠2at the A=0.05level based on the confidence interval?

(a) None. We cannot carry out the test without the original data.

(b) None. We cannot draw a conclusion at the A=0.05level since this test is connected to the 97.5%confidence interval.

(c) None. Confidence intervals and significance tests are unrelated procedures.

(d) We would reject H0at level A=0.05.

(e) We would fail to reject H0at level A=0.05.
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