Question

• For each hypothesis test, you must state (a) hypotheses, (b) test statistic, p-value, (c) rejection rule, and (d) both parts of the conclusion. It is only necessary to calculate the effect size if the problem calls for it. Use a .05 level of significance for all hypothesis tests. Use StatCrunch to complete all hypothesis tests and confidence intervals. Make sure you copy and paste the relevant output for the solutions.
• Honor code expectations: you are not allowed any collaboration or discussion, regardless of how minor, with anyone about this exam.

1. (11 points) Several engaged couples getting married were asked their religion and the number of children they plan to have. A sociologist wants to know if the mean number of children couples plan to have is different by religion.

Religion A	Religion B	Religion C	Religion D
3	2	6	3
3	3	1	3
1	3	2	2
2	5	4	1
4	1	3	2
2	1	1	2
3	2	2	4

1. Test whether the mean number of children differs by religion.
2. Calculate the coefficient of determination. Interpret it, both in terms of the size and what it tells about the variability.

Answer 1

Solution:

We are given the following data set:

Religion A	Religion B	Religion C	Religion D
3	2	6	3
3	3	1	3
1	3	2	2
2	5	4	1
4	1	3	2
2	1	1	2
3	2	2	4

Part(a)

We have to test whether the mean number of children differs by religion.

Our Null hypothesis is, H0: The mean number of children does not differ by religion.

The Alternative hypothesis is, H1: The mean number of children differs by religion.

So, we will test the mentioned hypothesis using One-Way Single-factor ANOVA.

So, we perform One-Way Single-factor ANOVA on the given data set and obtain the following output:

ANOVA: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Religion A	7	18	2.571429	0.952381
Religion B	7	17	2.428571	1.952381
Religion C	7	19	2.714286	3.238095
Religion D	7	17	2.428571	0.952381

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	0.392857	3	0.130952	0.073826	0.973461	3.008787
Within Groups	42.57143	24	1.77381
Total	42.96429	27

We see that the value of the F statistics is, F = 0.073826.

The critical F value at 0.05 level of significance is, F crit = 3.008787.

So, F = 0.073826 < 3.008787 = F crit.

Hence, we fail to reject the null hypothesis, " H0: The mean number of children does not differ by religion " at 0.05 level of significance.

Part(b)

The Between Groups sum of squares is = 0.392857.

The Within Groups sum of squares is = 42.57143.

The total sum of squares is = 42.96429.

The coefficient of determination is =

So, it tells that only 0.9144% of the variability is explained by the model.