Chapter 11.1, Problem 25BB

* Assumed mid-point

$\bar{x}=\frac{\Sigma fx}{n}=\frac{39825}{180}=\pounds 221.25$

$\text{s}=\sqrt{\left[\frac{\Sigma f{x}^2}{n-1}-\frac{{(\Sigma fx)}^2}{n(n-1)}\right]}=\sqrt{\left[\frac{10\text{ 244375}}{179}-\frac{{(39\text{ 825})}^2}{180\times 179}\right]}=\pounds 89.48$

25. Testing Goodness-of-Fit with a Normal Distribution Refer to Data Set 1 “Body Data” in Appendix B for the heights of females.

a. Enter the observed frequencies in the table above.

b. Assuming a normal distribution with mean and standard deviation given by the sample mean and standard deviation, use the methods of Chapter 6 to find the probability of a randomly selected height belonging to each class.

c. Using the probabilities found in part (b), find the expected frequency for each category.

d. Use a 0.01 significance level to test the claim that the heights were randomly selected from a normally distributed population. Does the goodness-of-fit test suggest that the data are from a normally distributed population?