Solutions

Please note that the steps show rounded numbers, but that the final answers to the problems are calculated without rounding.

Problem Part Solution
1 - The requirements are met because all expected counts are greater than or equal to five
2 - barchart
3 - \(H_0: \text{Religiosity and frequency of anger are independent}\)
\(H_a: \text{Religiosity and frequency of anger are not independent}\)
4 - \(\chi^2 = 23.474\)
\(df = 4\)
5 - \(\text{P-value} = 0.0001\)
6 - reject the null hypothesis
7 - There is sufficient evidence to suggest that religiosity and frequency of anger at something beyond one’s control are not independent.
8 - The requirements are met because all expected counts are greater than or equal to five
9 - barchart
10 - \(H_0: \text{Family structure and whether a girl goes to college are independent}\)
\(H_a: \text{Family structure and whether a girl goes to college are not independent}\)
11 - \(\chi^2 = 10.357\)
\(df = 3\)
12 - \(\text{P-value} = 0.016\)
13 - reject the null hypothesis
14 - There is sufficient evidence to suggest that family structure and whether a girl goes to college are not independent
15 - The requirements are met because all expected counts are greater than or equal to five
16 - barchart
17 - \(H_0: \text{Gender and PhD status are independent}\)
\(H_a: \text{Gender and PhD status are not independent.}\)
18 - \(\chi^2 = 1.932\)
\(df = 2\)
19 - \(\text{P-value} = 0.381\)
20 - fail to reject the null hypothesis
21 - There is insufficient evidence to conclude that a student’s gender and status in a PhD program are not independent.