# Question: Consider the sample of 65 payment times given in Table

Consider the sample of 65 payment times given in Table 2.4 (page 42). 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 x-bar = 18.1077 and that s = 3.9612 for the payment time data. Use these values to compute the intervals

(1) Less than x-bar – 2s

(2) x-bar – 2s < x-bar – s

(3) x-bar – < x-bar

(4) x-bar < x-bar + s

(5) x-bar + s < x-bar + 2s

(6) Greater than x-bar + 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 1. 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 a, 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?

a. It can be shown that x-bar = 18.1077 and that s = 3.9612 for the payment time data. Use these values to compute the intervals

(1) Less than x-bar – 2s

(2) x-bar – 2s < x-bar – s

(3) x-bar – < x-bar

(4) x-bar < x-bar + s

(5) x-bar + s < x-bar + 2s

(6) Greater than x-bar + 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 1. 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 a, 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?

## Answer to relevant Questions

Consider the sample of 60 bottle design ratings given in Table 1.5 (page 10). Use these data to carry out a chi-square goodness-of-fit test to determine whether the population of all bottle design ratings is normally ...In recent years major efforts have been made to standardize accounting practices in different countries; this is called harmonization. In an article in Accounting and Business Research, Emmanuel N. Emenyonu and Sidney J. ...In an article in Accounting and Business Research, Meier, Alam, and Pearson studied auditor lobbying on several proposed U. S. accounting standards that affect banks and savings and loan associations. As part of this study, ...In the Journal of Marketing Research (November 1996), Gupta studied the extent to which the purchase behavior of scanner panels is representative of overall brand preferences. A scanner panel is a sample of households whose ...The Excel output of a simple linear regression analysis of the data set for this case (see Table 13.4 on page 476) is given in Figure 13.12. Recall that a labeled Excel regression output is on page 482.Post your question