One can show that twosample tests are a special case of ANOV

One can show that two-sample tests are a special case of ANOVA. Using the data in Problem #2 perform ANOVA. -- Data is :: A sample of hourly wages of fast food chain workers for two cities are as follows:

City A: 5, 7, 9 City B: 10, 14, 15

1. Construct the ANOVA summary table. Calculation for SS(total) = 76.

2. Show all steps of hypothesis testing.

3. Based on your conclusion in part (b) and without calculating the 95% confidence interval for the mean difference between City A and City B hourly wages, would a mean difference of 0 be found within the confidence interval or outside of the confidence interval? Briefly explain.

4. Compare F-statistic with (t-statistic)2 from Problem #2. What can you say about your finding?

Solution

1. We have carried out ANOVA in MS -EXCEL Using the add-in Data Analysis.

2.

Null Hypothesis : hourly wages of the fast food chain workers of the two cities are same

Alternative Hypothesis : hourly wages of the fast food chain workers of the two cities are different

From anova table we have F statistic 9.818182 and critical F value 7.708647 . Since the test statistic has numerically higher value than critical F , we reject the null hypothesis. Thus the hourly wages of fast food chain workers of the two cities are different.

3.

Mean difference of 0 will lie outside the 95% confidence interval since the hourly wages are different for both cities.

4.

T-test using data analysis gives following results.

Here F statistic and the square of t- test statistic has the same numerical value.