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Chapter 9: Q6 (page 424)

Interpreting Displays.

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

Treating Carpal Tunnel Syndrome Carpal tunnel syndrome is a common wrist complaintresulting from a compressed nerve, and it is often the result of extended use of repetitive wristmovements, such as those associated with the use of a keyboard. In a randomized controlledtrial, 73 patients were treated with surgery and 67 were found to have successful treatments.Among 83 patients treated with splints, 60 were found to have successful treatments (based ondata from “Splinting vs Surgery in the Treatment of Carpal Tunnel Syndrome,” by Gerritsenet al., Journal of the American Medical Association, Vol. 288, No. 10). Use the accompanyingStatCrunch display with a 0.01 significance level to test the claim that the success rate is better with surgery.

Short Answer

Expert verified

There is sufficient evidence to support the claim that the success rate for surgery is better than the success rate of splints in the treatment at a 0.01 level of significance.

Step by step solution

01

Given information

The output is known

02

Describe the hypothesis to be tested

Let p1be the population proportion of success rate in splinting and p2be population proportion of success rate in surgery.

Mathematically, the test hypothesis is,

H0:p1=p2H1:p1<p2

The test is one-tailed.

03

State the result

The decision rule:

If p value is less than the level of significance then reject the null hypothesis atlevel of significance.

Here, the p-value is 0.0009 which is less than the level of significance.

Therefore, reject null hypothesis at 0.01significance level.

04

Interpret the result

Therefore, there is sufficient evidence to support the claim that the success rate for surgery is better than the success rate of splinting.

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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 5–20, 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 “Table” answers based on Table A-3 with df equal to the smaller of n1−1 and n2−1.)

Color and Cognition Researchers from the University of British Columbia conducted a study to investigate the effects of color on cognitive tasks. Words were displayed on a computer screen with background colors of red and blue. Results from scores on a test of word recall are given below. Higher scores correspond to greater word recall.

a. Use a 0.05 significance level to test the claim that the samples are from populations with the same mean.

b. Construct a confidence interval appropriate for the hypothesis test in part (a). What is it about the confidence interval that causes us to reach the same conclusion from part (a)?

c. Does the background color appear to have an effect on word recall scores? If so, which color appears to be associated with higher word memory recall scores?

Red Background n = 35, x = 15.89, s = 5.90

Blue Background n = 36, x = 12.31, s = 5.48

Testing Claims About Proportions. In Exercises 7–22, 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.

Is Echinacea Effective for Colds? Rhinoviruses typically cause common colds. In a test of the effectiveness of Echinacea, 40 of the 45 subjects treated with Echinacea developed rhinovirus infections. In a placebo group, 88 of the 103 subjects developed rhinovirus infections (based on data from “An Evaluation of Echinacea Angustifolia in Experimental Rhinovirus Infections,” by Turner et al., New England Journal of Medicine, Vol. 353, No. 4). We want to use a 0.05 significance level to test the claim that Echinacea has an effect on rhinovirus infections.

a. Test the claim using a hypothesis test.

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

c. Based on the results, does Echinacea appear to have any effect on the infection rate?

Testing Claims About Proportions. In Exercises 7–22, 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

Question:Headache Treatment In a study of treatments for very painful “cluster” headaches, 150 patients were treated with oxygen and 148 other patients were given a placebo consisting of ordinary air. Among the 150 patients in the oxygen treatment group, 116 were free from head- aches 15 minutes after treatment. Among the 148 patients given the placebo, 29 were free from headaches 15 minutes after treatment (based on data from “High-Flow Oxygen for Treatment of Cluster Headache,” by Cohen, Burns, and Goads by, Journal of the American Medical Association, Vol. 302, No. 22). We want to use a 0.01 significance level to test the claim that the oxygen treatment is effective.

a. Test the claim using a hypothesis test.

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

c. Based on the results, is the oxygen treatment effective?

Testing Claims About Proportions. In Exercises 7–22, 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.

License Plate Laws The Chapter Problem involved passenger cars in Connecticut and passenger cars in New York, but here we consider passenger cars and commercial trucks. Among2049 Connecticut passenger cars, 239 had only rear license plates. Among 334 Connecticuttrucks, 45 had only rear license plates (based on samples collected by the author). A reasonable hypothesis is that passenger car owners violate license plate laws at a higher rate than owners of commercial trucks. Use a 0.05 significance level to test that hypothesis.

a. Test the claim using a hypothesis test.

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