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Chapter 9: Q6BSC (page 414)

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 鈥淪plinting vs Surgery in the Treatment of Carpal Tunnel Syndrome,鈥� 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\({p_1}\)be the population proportion of success rate in splinting and\({p_2}\)be population proportion of success rate in surgery.

Mathematically, the test hypothesis is,

\(\begin{array}{l}{H_0}:{p_1} = {p_2}{\rm{ }}\\{H_1}:{p_1} < {p_2}\end{array}\)

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 at\({\rm{\alpha }}\)level of significance.

Here, the p-value is 0.0009 which is less than the level of significance\(\alpha = 0.01\).

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

We have specified a margin of error, a confidence level, and a likely range for the observed value of the sample proportion. For each exercise, obtain a sample size that will ensure a margin of error of at most the one specified (provided of course that the observed value of the sample proportion is further from 0.5than the educated guess).Obtain a sample size that will ensure a margin of error of at most the one specified.

marginoferror=0.04;confidencelevel=99%;likelyrange=0.7orless

Independent and Dependent Samples Which of the following involve independent samples?

a. Data Set 14 鈥淥scar Winner Age鈥� in Appendix B includes pairs of ages of actresses and actors at the times that they won Oscars for Best Actress and Best Actor categories. The pair of ages of the winners is listed for each year, and each pair consists of ages matched according to the year that the Oscars were won.

b. Data Set 15 鈥淧residents鈥� in Appendix B includes heights of elected presidents along with the heights of their main opponents. The pair of heights is listed for each election.

c. Data Set 26 鈥淐ola Weights and Volumes鈥� in Appendix B includes the volumes of the contents in 36 cans of regular Coke and the volumes of the contents in 36 cans of regular Pepsi.

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.

Tennis Challenges Since the Hawk-Eye instant replay system for tennis was introduced at the U.S. Open in 2006, men challenged 2441 referee calls, with the result that 1027 of the calls were overturned. Women challenged 1273 referee calls, and 509 of the calls were overturned. We want to use a 0.05 significance level to test the claim that men and women have equal success in challenging calls.

a. Test the claim using a hypothesis test.

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

c. Based on the results, does it appear that men and women have equal success in challenging calls?

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.

Cardiac Arrest at Day and Night A study investigated survival rates for in hospital patients who suffered cardiac arrest. Among 58,593 patients who had cardiac arrest during the day, 11,604 survived and were discharged. Among 28,155 patients who suffered cardiac arrest at night, 4139 survived and were discharged (based on data from 鈥淪urvival from In-Hospital Cardiac Arrest During Nights and Weekends,鈥� by Puberty et al., Journal of the American Medical Association, Vol. 299, No. 7). We want to use a 0.01 significance level to test the claim that the survival rates are the same for day and night.

a. Test the claim using a hypothesis test.

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

c. Based on the results, does it appear that for in-hospital patients who suffer cardiac arrest, the survival rate is the same for day and night?

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.

Are Seat Belts Effective? A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2823 occupants not wearing seat belts, 31 were killed. Among 7765 occupants wearing seat belts, 16 were killed (based on data from 鈥淲ho Wants Airbags?鈥� by Meyer and Finney, Chance, Vol. 18, No. 2). We want to use a 0.05 significance level to test the claim that seat belts are effective in reducing fatalities.

a. Test the claim using a hypothesis test.

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

c. What does the result suggest about the effectiveness of seat belts?
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