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Chapter 9: Q5 (page 423)

Interpreting Displays.

In Exercises 5 and 6, use the results from the given displays.

Testing Laboratory Gloves, The New York Times published an article about a study by Professor Denise Korniewicz, and Johns Hopkins researched subjected laboratory gloves to stress. Among 240 vinyl gloves, 63% leaked viruses; among 240 latex gloves, 7% leaked viruses. See the accompanying display of the Statdisk results. Using a 0.01 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves.

Short Answer

Expert verified

Reject the null hypothesis under 0.01 significance level.

There is sufficient evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.

Step by step solution

01

Given information

The output for the test

02

Describe the hypothesis to be tested.

Let p1be the population proportion of virus leak rate of vinyl gloves and p2be population proportion of virus leak rate of latex gloves.

Mathematically, the test hypothesis is:

H0:p1=p2H1:p1>p2

03

State the result

From the output the p-value is 0.0000.

Decision rule:

If the p-value is smaller than 0.01, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

As the p-value is lesser than 0.01, reject the null hypothesis.

Thus, there is enough evidence to conclude that the leak rate is greater in vinyl gloves than latex.

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Most popular questions from this chapter

Using Confidence Intervals

a. Assume that we want to use a 0.05 significance level to test the claim that p1 < p2. Which is better: A hypothesis test or a confidence interval?

b. In general, when dealing with inferences for two population proportions, which two of the following are equivalent: confidence interval method; P-value method; critical value method?

c. If we want to use a 0.05 significance level to test the claim that p1 < p2, what confidence level should we use?

d. If we test the claim in part (c) using the sample data in Exercise 1, we get this confidence interval: -0.000508 < p1 - p2 < - 0.000309. What does this confidence interval suggest about the claim?

In Exercises 5鈥�20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with 鈥淭able鈥� answers based on Table A-3 with df equal to the smaller of n1鈭�1 and n2鈭�1.)Coke and Pepsi Data Set 26 鈥淐ola Weights and Volumes鈥� in Appendix B includes volumes of the contents of cans of regular Coke (n = 36, x = 12.19 oz, s = 0.11 oz) and volumes of the contents of cans of regular Pepsi (n = 36, x = 12.29 oz, s = 0.09 oz).

a. Use a 0.05 significance level to test the claim that cans of regular Coke and regular Pepsi have the same mean volume.

b. Construct the confidence interval appropriate for the hypothesis test in part (a).

c. What do you conclude? Does there appear to be a difference? Is there practical significance?

Testing Claims About Proportions. In Exercises 7鈥�22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.

Smoking Cessation Programs Among 198 smokers who underwent a 鈥渟ustained care鈥� program, 51 were no longer smoking after six months. Among 199 smokers who underwent a 鈥渟tandard care鈥� program, 30 were no longer smoking after six months (based on data from 鈥淪ustained Care Intervention and Postdischarge Smoking Cessation Among Hospitalized Adults,鈥� by Rigotti et al., Journal of the American Medical Association, Vol. 312, No. 7). We want to use a 0.01 significance level to test the claim that the rate of success for smoking cessation is greater with the sustained care program.

a. Test the claim using a hypothesis test.

b. Test the claim by constructing an appropriate confidence interval.

c. Does the difference between the two programs have practical significance?

True?For the methods of this section, which of the following statements are true?

a.When testing a claim with ten matched pairs of heights, hypothesis tests using the P-valuemethod, critical value method, and confidence interval method will all result in the same conclusion.

b.The methods of this section are robustagainst departures from normality, which means that the distribution of sample differences must be very close to a normal distribution.

c.If we want to use a confidence interval to test the claim that\({{\bf{\mu }}_{\bf{d}}}{\bf{ < 0}}\)with a 0.01 significancelevel, the confidence interval should have a confidence level of 98%.

d.The methods of this section can be used with annual incomes of 50 randomly selected attorneysin North Carolina and 50 randomly selected attorneys in South Carolina.

e.With ten matched pairs of heights, the methods of this section require that we use n= 20.

Magnet Treatment of Pain People spend around $5 billion annually for the purchase of magnets used to treat a wide variety of pains. Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results given below are among the results obtained in the study (based on data from 鈥淏ipolar Permanent Magnets for the Treatment of Chronic Lower Back Pain: A Pilot Study,鈥� by Collacott, Zimmerman, White, and Rindone, Journal of the American Medical Association, Vol. 283, No. 10). Higher scores correspond to greater pain levels.

a. Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment (similar to a placebo).

b. Construct the confidence interval appropriate for the hypothesis test in part (a).

c. Does it appear that magnets are effective in treating back pain? Is it valid to argue that magnets might appear to be effective if the sample sizes are larger?

Reduction in Pain Level after Magnet Treatment: n = 20, x = 0.49, s = 0.96

Reduction in Pain Level after Sham Treatment: n = 20, x = 0.44, s = 1.4

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