Consider the sample of 65 payment times given in Table 2.4. Use these data to carry out a chi square goodness of fit test to test whether the population of all payment times is normally distributed by doing the following:
a. It can be shown that  = 18.1077 and that s = 3.9612 for the payment time data. Use these values to compute the intervals
(1) Less than  - 2s
(4)  <  + s
(2)  - 2s <  - s
(5)  + s <  + 2s
(3)  - s < 
(6) Greater than  + 2s
b. Assuming that the population of all payment times is normally distributed, find the probability that a randomly selected payment time will be contained in each of the intervals found in part a. Use these probabilities to compute the expected frequency under the normality assumption for each interval.
c. Verify that the average of the expected frequencies is at least 5 and that the smallest expected frequency is at least l. What does this tell us?
d. Formulate the null and alternative hypotheses for the chi-square test of normality.
e. For each interval given in part α, find the observed frequency. Then calculate the chi-square statistic needed for the chi-square test of normality.
f. Use the chi-square statistic to test normality at the .05 level of significance. What do you conclude?