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Chapter 9: Q.7 (page 597)

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.

Short Answer

Expert verified

The correct answer is (e).

Step by step solution

01

Given Information

H0:μ=2

Ha:μ≠2

95%confidence interval: (1.7,3.5).

02

Explanation

The confidence interval contains the value 2 , the value 2 is a likely candidate for the population mean μ and thus we fail to reject the null hypothesis H0.

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Most popular questions from this chapter

You are testing H0:μ=10against Hα:μ≠10based on an SRS of 15tobservations from a Normal population. What values of the statistic are statistically significant at theα=0.005level?

(a) t>3.326

(b) t>3.286

(c) t>2.977

(d) t<-3.326ort>3.326

(c)t<-3.286ort>3.286

An SRS of 100 postal employees found that the average time these employees had worked at the postal service was 7years with standard deviation 2years. Do these data provide convincing evidence that the mean time of employment M for the population of postal employees has changed from the value of 7.5 that was true 20years ago? To determine this, we test the hypotheses H0:μ=7.5versus Ha:μ≠7.5using a one-sample ttest. What conclusion should we draw at the 5%significance level?

(a) There is convincing evidence that the mean time working with the postal service has changed.

(b) There is not convincing evidence that the mean time working with the postal service has changed.

(c) There is convincing evidence that the mean time working with the postal service is still 7.5 years.

(d) There is convincing evidence that the mean time working with the postal service is now 7years.

(e) We cannot draw a conclusion at the 5% significance level. The sample size is too small.

A government report says that the average amount of money spent per U.S. household per week on food is about \(158. A random sample of 50households in a small city is selected, and their weekly spending on food is recorded. The Minitab output below shows the results of requesting a confidence interval for the population mean M. An examination of the data reveals no outliers.

(a) Explain why the Normal condition is met in this case.

(b) Can you conclude that the mean weekly spending on food in this city differs from the national figure of\)158? Give appropriate evidence to support your answer.

What is significance good for? Which of the following questions does a significance test answer? Justify your answer.

(a) Is the sample or experiment properly designed?

(b) Is the observed effect due to chance?

(c) Is the observed effect important?

Do you have ESP? A researcher looking for evidence of extrasensory perception (ESP) tests 500subjects. Four of these subjects do significantly better P<0.01than random guessing.

(a) Is it proper to conclude that these four people have ESP? Explain your answer.

(b) What should the researcher now do to test whether any of these four subjects have ESP?
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