Question

a physical therapist wanted to know whether the mean step pulse of men was less than the mean step pulse of women she randomly selected 55 men and 79 women to participate in the study each subject was required to step up and down a 6 - inch platform. the pulse of each subject was then recorded. the following results were obtained. (c) what is the 98% confidence interval for the mean difference in pulse rates of men versus women? the lower bound is - 11.29 the upper bound is - 0.51 (round to two decimal places as needed.) interpret this result. a. 98% percent of the time the mean difference is in the confidence interval b. we are 98% confident that the means are in the confidence interval c. we are 98% confident that the mean difference is in the confidence interval d. 98% percent of the time the means are in the confidence interval

Explanation:

A confidence interval gives a range of values within which we are confident the true population parameter (in this case, the mean difference in pulse rates) lies. The interpretation of a \(98\%\) confidence interval is that we are \(98\%\) confident that the interval contains the true population parameter.

• Option A is incorrect because it refers to the mean difference being in the interval \(98\%\) of the time, which is a misinterpretation. Confidence intervals are about our level of confidence in capturing the true parameter, not about the frequency of the difference being in the interval over repeated samples in that way.
• Option B is wrong as it says the means are in the interval. The confidence interval is for the mean difference (\(\mu_{\text{Men}}-\mu_{\text{Women}}\)), not for the individual means.
• Option C is correct. The \(98\%\) confidence interval for \(\mu_{\text{Men}}-\mu_{\text{Women}}\) means we are \(98\%\) confident that the mean difference (men's mean pulse - women's mean pulse) is within the given interval \((- 11.29,-0.51)\).
• Option D is incorrect for the same reason as Option B. It refers to the means being in the interval, while the interval is for the mean difference.

Answer:

C. We are 98% confident that the mean difference is in the confidence interval.