Final answer:
To determine if geography affects how much money people spend per holiday gift, an ANOVA test can be used. The null hypothesis is that geography does not affect spending, and the alternative hypothesis is that it does.
The critical value is determined using the degrees of freedom and significance level. The statistic is calculated by finding the sum of squares between groups (SSB), sum of squares within groups (SSW), and the F statistic.
The decision is made by comparing the calculated F statistic to the critical value.
If the null hypothesis is rejected, further analysis can be done to calculate effect size and perform post-hoc tests.
Step-by-step explanation:
In order to determine if geography affects how much money people spend per holiday gift, we can use an analysis of variance (ANOVA) test. This test allows us to compare the means of multiple groups to see if they are significantly different from each other.
a) The statistical test to solve this problem is ANOVA.
b) The null hypothesis would be that geography does not affect how much money people spend per holiday gift, and the alternative hypothesis (Ha) would be that geography does affect how much money people spend per holiday gift.
c) To locate the critical value that defines the critical region, we need to determine the degrees of freedom and the significance level.
d) To calculate the statistic for the ANOVA test, we need to calculate the sum of squares between groups (SSB), the sum of squares within groups (SSW), and the F statistic.
c) To make a decision with respect to the null, we compare the calculated F statistic to the critical value. If the calculated F statistic is larger than the critical value, we reject the null hypothesis and conclude that geography does affect how much money people spend per holiday gift. If the calculated F statistic is smaller than the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that geography affects how much money people spend per holiday gift.
B) If the null hypothesis is rejected, it would be important to calculate the effect size using measures like eta-squared or omega-squared. Additionally, a post-hoc test, such as Tukey's HSD or Scheffe's test, can be performed to determine which specific groups differ significantly from each other.