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Chapter 9: Q.8 (page 595)

Radon detectors Radon is a colorless, odorless gas that is naturally released by rocks and soils and may concentrate in tightly closed houses. Because radon is slightly radioactive, there is some concern that it may be a health hazard. Radon detectors are sold to homeowners worried about this risk, but the detectors may be inaccurate. University researchers placed a random sample of 11detectors in a chamber where they were exposed to 105picocuries per liter of radon over 3days. A graph of the radon readings from the 11detectors shows no strong skewness or outliers. The Minitab output below shows the results of a one-sample t interval. Is there significant evidence at the 10%level that the mean reading 渭differs from the true value 105? Give appropriate evidence to support your answer.

Short Answer

Expert verified

The confidence interval contains 105, there is not sufficient evidence at the 10% level to support the claim.

Step by step solution

01

Given Information

90% confidence interval: (99.61,110.03).

02

Explanation

Determine the hypotheses:

H0:渭=105

Ha:渭鈮�105

A 90%confidence interval corresponds with a significance test at the 10%significance level.

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Most popular questions from this chapter

Improving health A large company's medical director launches a health promotion campaign to encourage employees to exercise more and eat better foods. One measure of the effectiveness of such a program is a drop in blood pressure. The director chooses a random sample of 50employees and compares their blood pressures from physical cams given before the campaign and again a year later. The mean change (after - before) in systolic blood pressure for these 50employees is -6and the standard deviation is 19.8.

(a) Do these data provide convincing evidence of an average decrease in blood pressure among all of the company's employees during this year? Carry out a test at the 伪=0.05significance level.

(b) Can we conclude that the health campaign caused a decrease in blood pressure? Why or why not?

Describe a Type II error in this setting.

A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of one inch could be increased by

(a) using only volunteers from the basketball team in the experiment.

(b) using A=0.01 instead of A=0.05.

(c) using A=0.05 instead of A=0.01.

(d) giving the drug to 25 randomly selected students instead of 50.

(e) using a two-sided test instead of a one-sided test.

Tests and CIs The P-value for a one-sided test of the null hypothesisH0:渭=15is 0.03.

(a) Does the 99%confidence interval for 渭include 15? Why or why not?

(b) Does the 95%confidence interval for 渭include 15? Why or why not?

Refer to Exercise 2. For Yvonne's survey, 96 students in the sample said they rarely or never argue with friends. A significance test yields a P-value of 0.0291.

(a) Interpret this result in context.

(b) Do the data provide convincing evidence against the null hypothesis? Explain.
See all solutions

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