Question

researchers examine the relationship between church attendance and hours spent on homework each week for a random sample of 80 high school students. students were grouped into four categories based on frequency of church attendance: never attend, attend infrequently, attend frequently, attend very frequently. null hypothesis: for high school students, there is a no relationship between church attendance and hours spent on homework each week (i.e. the mean hours spent on homework each week are the same for the four populations defined by church-going frequency.) alternative hypothesis: for high school students, there is a relationship between church attendance and hours spent on homework each week (i.e. the mean hours spent on homework each week differ for the four populations defined by church-going frequency.) analysis of variance results: responses: homework factors: attendchurch response statistics by factor attendchurch n mean std. dev. std. error freq 26 9.4 5.8 1.1 infreq 27 6.4 4.4 0.9 never 10 7.9 5.4 1.7 veryfreq 18 8.9 7.1 1.7 anova table source df ss ms f-stat p-value attendchurch 3 136.05632 45.352105 1.4145498 0.245 error 77 2468.7091 32.061157 total 80 2604.7654 to check conditions for use of the anova f-test which ratio is useful? [ select ] to check conditions for use of the anova f-test, we need to examine histograms of the homework hours for how many of the samples? [ select ] assuming that the conditions are met for use of the anova f-test, which conclusion does the data support? [ select ]

Answer 1

To check for homogeneity of variances in an ANOVA F-test, the ratio of the largest to the smallest variances is useful. Histograms for all four groups are needed to examine normality. With a p-value of 0.245, the null hypothesis is not rejected, indicating no sufficient evidence of a relationship between church attendance and homework hours.

Step-by-step explanation:

To check conditions for the use of the ANOVA F-test, the ratio of the largest to the smallest variances in the sample is often used, as it helps to verify the assumption of homogeneity of variances. This condition requires that the variances within each of the populations are approximately equal.

For verifying normality and other assumptions of an ANOVA test, histograms of the homework hours would need to be examined for each of the groups defined by the frequency of church attendance. Therefore, we would need to look at four histograms corresponding to the 'never attend', 'attend infrequently', 'attend frequently', and 'attend very frequently' groups.

Assuming that conditions for the ANOVA F-test are met, we look at the p-value in the ANOVA table to make our decision about the hypotheses. With a p-value of 0.245, which is greater than the usual significance level of 0.05, we fail to reject the null hypothesis. This suggests that the data does not provide sufficient evidence to support the claim that the mean hours spent on homework each week differ for the four populations defined by church-going frequency.

Answer 2

Step-by-step explanation:

To check conditions for the use of the ANOVA F-test, the ratio of the largest sample variance to the smallest sample variance is useful.

To check conditions for the use of the ANOVA F-test, we need to examine histograms of the homework hours for all four samples (never attend, attend infrequently, attend frequently, and attend very frequently).

Assuming that the conditions are met for the use of the ANOVA F-test, the data do not support the alternative hypothesis that there is a relationship between church attendance and hours spent on homework each week. The p-value of 0.245 is greater than the typical significance level of 0.05, indicating that there is not enough evidence to reject the null hypothesis that there is no relationship between church attendance and hours spent on homework each week.