Question

According to a report sponsored by the National Center for Health Statistics, 75% of American women have been married by the age of 30. Patrice, a single woman of 32 who has never been married, claims that this percentage is too high. To test her claim, she surveys 125 women between the ages of 18 and 30 and finds that 92 of them have been married. Does this evidence support Patrice’s claim that less than 75% of women 30 years or old or younger have been married? Use the 0.10 level of significance.

Answer 1

a)

point estimate = Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.75
Alternative Hypothesis, Ha: p < 0.75

Rejection Region
This is left tailed test, for α = 0.1
Critical value of z is -1.28.
Hence reject H0 if z < -1.28

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.736 - 0.75)/sqrt(0.75*(1-0.75)/125)
z = -0.36

P-value Approach
P-value = 0.3594
As P-value >= 0.1, fail to reject null hypothesis.

There is not sufficient evidence to conclude that less than 75% of women 30 years or old or younger have been married