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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

(a) State hypotheses for a significance test to determine whether first responders are arriving within 8 minutes of the call more often. Be sure to define the parameter of interest.

(b) Describe a Type I error and a Type II error in this setting and explain the consequences of each.

(c) Which is more serious in this setting: a Type I error or a Type II error? Justify your answer.

(d) If you sustain a life-threatening injury due to a vehicle accident, you want to receive medical treatment as quickly as possible. Which of the two significance tests鈥�H0:渭=6.7versusHa:渭<6.7 or the one from part (a) of this exercise鈥攚ould you be

more interested in? Justify your answer.

Significance tests A test ofH0:p=0.5versus Ha : p >0.5 has test statistic z=2.19.

(a) What conclusion would you draw at the 5 % significance level? At the 1 % level?

(b) If the alternative hypothesis were H0:p鈮�0.5what conclusion would you draw at the 5% significance level? At the 1 % level?

Power A drug manufacturer claims that fewer than 10% of patients who take its new drug for treating Alzheimer's disease will experience nausea. To test this claim, a significance test is carried out of

H0:p=0.10Ha:p<0.10

You learn that the power of this test at the 5 % significance level against the alternative p=0.08 is 0.64.

(a) Explain in simple language what "power =0.64" means in this setting.

(b) You could get higher power against the same alternative with the same 伪 by changing the number of measurements you make. Should you make more measurements or fewer to increase power? Explain.

(c) If you decide to use 伪=0.01in place of 伪=0.05, with no other changes in the test, will the power increase or decrease? Justify your answer.

(d) If you shift your interest to the alternative p= 0.07 with no other changes, will the power increase or decrease? Justify your answer.

Losing weight A Gallup Poll found that 59% of the people in its sample said 鈥淵es鈥� when asked, 鈥淲ould you like to lose weight?鈥� Gallup announced: 鈥淔or

results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is 魛伅3 percentage points.鈥�16 Can we use this interval to conclude that the actual proportion of U.S. adults who would say they want to lose weight differs from 0.55? Justify your answer.

An investor with a stock portfolio worth several hundred thousand dollars sued his broker due to the low returns he got from the portfolio at a time when the stock market did well overall. The investor鈥檚 lawyer wants to compare the broker鈥檚 performance against the market as a whole. He collects data on the broker鈥檚 returns for a

random sample of 36 weeks. Over the 10-year period that the broker has managed portfolios, stocks in the Standard & Poor鈥檚 500 index gained an average of 0.95% per month. The Minitab output below displays descriptive statistics for these data, along with the results of a significance test.

(a) Determine whether there are any outliers. Show your work.

(b) Interpret the P-value in context.

(c) Do these data give convincing evidence to support the lawyer鈥檚 case? Carry out a test to help you answer this question.
See all solutions

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