Question

The US Census Bureau looked at the gap between married and unmarried Americans in 1950 and 2019. The following table shows the numbers (actually percentages) for 1950 and 2019.

Marital Status	1950	2019
Married	66.6	52.3
Never married	23.0	32.4
Divorced	2.3	9.5
Widowed	8.0	5.7

Source 1950 Decennial Census and the Current Population Survey Annual Social and Economic Supplement, “Understanding the Census”, March 2020, p. 35.

Assume this is a related sample test (paired t-test). The mean difference is 0.025, the standard deviation difference S_D is 10.7803, and the p-value is 0.9966. Assuming that the population variances are equal, is there evidence of a difference in in the marital status of Americans between 1950 and 2019 (α=.01)?

State the null hypothesis
State the alternative hypothesis
What critical values should be used?
What is the test statistic?
What is the p-value?
Interpret the meaning of the p-value
Should the null hypothesis be rejected
What is the conclusion?
State one of the assumptions needed
State the degrees of freedom

Answer 1