Question

True or False Question

The percentage of males in 1986 who are 18-19 years old and married was 3.7%. To test whether or not this percentage had increased in 2015, a random sample of 300 males aged 18-19 was taken; 20 of which were married. Using a level of significance of α= 0.05, we test the hypothesis H0 that the proportion that is married is 3.7%against the alternative that it is larger. Based on the data, the observed value of the corresponding test statistic is 2.722 and we reject H0.

True False

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.037

H_a : p > 0.037

Test statistic = z = 2.722

P(z > 2.722 ) = 1 - P(z < 2.722 ) = 1 - 0.9968

P-value = 0.0032

$\alpha$ = 0.05    

P-value < $\alpha$

Reject the H₀

True