Question

. A student wanted to study the ages of couples applying for marriage licenses in his county. He studied a sample of 96 marriage licenses and found that in 67 cases the husband was older than the wife. Do the sample data provide evidence that the husband is usually older than the wife among couples applying for marriage licenses in that county? Explain briefly and justify your answer using the methods studied in this course. Use α= 0.05 as the level of significance.

Answer 1

Null Hypothesis, 0.5

Alternative Hypothesis, 0.5

67/96 = 0.6979, n = 96

Here the significance level, 0.05. This is right tailed test; hence rejection region lies to the right. 1.64 i.e. P(z > 1.64) = 0.05

Reject H0 if test statistic, z > 1.645

Test statistic,

z = (0.6979 - 0.5)/sqrt(0.5*0.5/96)

z = 3.88

p-value = P(z > 3.88) = 0.0001

As p-value < 0.05, reject H0

There is sufficient evidence to conclude that the husband is usually older than the wife among couples applying for marriage licenses in that county