Question

In 1960, census results indicated that the age at which American men first married had a mean of 23.3 years. It is widely suspected that young people today are waiting longer to get married. A random sample of 40 men who married for the first time last year was studied. The men in this sample married at an average age of 25.9 years, with a standard deviation of 5.3 years. A histogram of the data is given to the right. Do these data provide evidence at the .05 level of significance that the mean age of first marriage for American men has increased? Be sure to assess the assumptions and interpret the results in context.

Answer 1

= 23.3

X_bar = 25.9

= 5.3

n= 40

1) Hypothesis:

H0 : = 23.3

H1 : ​​​​​​ > 23.3

2) test statistic Z

Z = (x_bar - ​​​​​​) /(/n)

= (25.9-23.3)/(5.3/40)

Z = 3.10

3) p value for Z test statistic is 0.001

P value = 0.001

4) conclusion :

The p value (0.001) is less than 0.05 level of significance that is reject null hypothesis. It sufficient evidence to conclude that the mean age of first marriage of American men has increased.