71 Are the mean number of times a month a person eats out th

71. Are the mean number of times a month a person eats out the same for whites, blacks, Hispanics and Asians? Suppose that Table 13.26 shows the results of a study. Table 13.26 Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.

Solution

The test hypothesis:

Ho: all means are equal (i.e. null hypothesis)

Ha: at least one mean is different (i.e. alternative hypothesis)

The test statistic is

F=0.89

The p-value of F test is 0.4711 (from F table)

Since the p-value is larger than 0.05, we do not reject the null hypothesis.

So we can conclude that the mean number of times a month a person eats out the same for whites, blacks, Hispanics and Asians

Mean	n	Std. Dev
5.2	5	2.28	White
3.0	4	1.83	Black
5.0	5	1.58	Hispanic
4.8	5	2.86	Asian
4.6	19	2.19	Total