Assume that the following data are from a random sample of the body temperatures of 55 healthy adults.
Use Excel or your calculator to compute the following, using the above data. Because the variability is small, be sure to carry out all calculations to at least four (4) decimal places.
(a) Find the sample mean, x .
(b) Find the sample standard deviation, s.
(c) Construct a 95% confidence interval for the true population mean for body temperatures of healthy adults.
(d) Replace one of the 98.6 data values with the number 986. Note that this is not possible as a healthy adult's body temperature (!) but it is a mistake that is easy to make when entering a large amount of data. Re-compute the values for the 95% confidence interval, and discuss the effect of outliers on the width of a confidence interval. Why do you think outliers have this effect on the confidence interval?
(e) Test the hypothesis that the true mean of the population of healthy adult body temperatures is exactly equal to 98.6º. Use a level of significance of 0.01 α = . Clearly state the null hypothesis, the alternative hypothesis, whether you used a one-tailed or two-tailed test, the value of your (standardized) test statistic, the actual p-value you obtained, and your conclusion (do you reject or fail to reject the null hypothesis and why).