Use the Following Information to Answer the Question $$\bar { x } = 14.5 \text { hours, } s = 1.2 \text { hours }$$

question 47

Multiple Choice

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants was taken and the mean finishing time was found to be 1.59 hours with a standard deviation of 0.30 hours.
-Suppose a consumer product researcher wanted to find out whether a highlighter lasted longer than the manufacturer's claim that their highlighters could write continuously for 14 hours. The Researcher tested 40 highlighters and recorded the number of continuous hours each highlighter
Wrote before drying up. Test the hypothesis that the highlighters wrote for more than 14 Continuous hours. Following are the summary statistics: $$\bar { x } = 14.5 \text { hours, } s = 1.2 \text { hours }$$ Report the test statistic, p-value, your decision regarding the null hypothesis. At the 5% Significance level, state your conclusion about the original claim. Round all values to the nearest
Thousandth.

• A) \(z = 9.583 ; p = 0.000 ^ { + }\); Reject the null hypothesis; there is strong evidence to suggest that the highlighters last longer than 14 hours.
• B) \(t = 2.635 ; p = 0.006\); Reject the null hypothesis; there is strong evidence to suggest that the highlighters last longer than 14 hours.
• C) \(\mathrm { z } = 9.583 ; \mathrm { p } = 0.000 ^ { + }\); Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last longer than 14 hours.
• D) \(t = 2.635 ; \mathrm { p } = 0.006\); Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last longer than 14 hours.

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