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# BA 303 - BUSINESS STATISTICS – Week 5: Learning Unit 2: Discussion 2: Chapter 7, Problem 46

**46. For the data in the Excel file Freshman College Data.**

**A. Use ANOVA to determine whether significant differences exist in the mean retention rate for the different colleges over the four-year period.**

**B. Use ANOVA to determine if significant differences exist in the mean ACT scores among the different colleges.**

**C. Use ANOVA to determine if significant differences exist in the mean SAT scores among the different colleges.**

**46. For the data in the Excel file Freshman College Data.**

**A. Use ANOVA to determine whether significant differences exist in the mean retention rate for the different colleges over the four-year period.**

Using ANOVA, we are trying to determine if there is any significant difference in mean retention rate of the different colleges. First, we set up our two hypotheses that we will be looking to prove.

H0= there is no significant differences in the mean retention rate for different colleges

H1= there is a significant difference in the mean retention rate for different colleges

We will assume that the level of significance is 0.05 and will reject the null hypothesis if the test statistic F is greater than the critical value for F. Using the ANOVA: single factor function in excel, we calculate the following data.

Based on this data, we see that the F statistic is 11.15 while the F critical value is 2.13 which means that the null hypothesis is rejected. This means that there is a significant difference in the mean retention rate for the different colleges over four years.

**B. Use ANOVA to determine if significant differences exist in the mean ACT scores among the different colleges.**

Using ANOVA, we are trying to determine if there is any significant difference in mean ACT scores of the different colleges. First, we set up our two hypotheses that we will be looking to prove.

H0= there is no significant differences in the mean ACT scores for different colleges

H1= there is a significant difference in the mean ACT scores for different colleges

We will assume that the level of significance is 0.05 and will reject the null hypothesis if the test statistic F is greater than the critical value for F. Using the ANOVA: single factor function in excel, we calculate the following data.

Based on this data, we see that the F statistic is 110.61 while the F critical value is 2.13 which means that the null hypothesis is rejected. This means that there is a significant difference in the mean ACT scores for the different colleges.

**C. Use ANOVA to determine if significant differences exist in the mean SAT scores among the different colleges.**

Using ANOVA, we are trying to determine if there is any significant difference in mean SAT scores of the different colleges. First, we set up our two hypotheses that we will be looking to prove.

H0= there is no significant differences in the mean SAT scores for different colleges

H1= there is a significant difference in the mean SAT scores for different colleges

We will assume that the level of significance is 0.05 and will reject the null hypothesis if the test statistic F is greater than the critical value for F. Using the ANOVA: single factor function in excel, we calculate the following data.

Based on this data, we see that the F statistic is 126.99 while the F critical value is 2.13 which means that the null hypothesis is rejected. This means that there is a significant difference in the mean ACT scores for the different colleges.