Question

The Department reported that 43% of US women work full time. Some believe that this percentage has increased. A random sample of 80 women resulted in that 42 of the women work full time. Conduct a hypothesis test at the 0.01 significance level to determine whether the proportion of US women who work full time has increased since 2016. What is the p-value, and what is the appropriate conclusion regarding the alternative hypothesis.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.43

Ha : p > 0.43

n = 80

x =42

= x / n = 42 / 80 = 0.52

P0 = 0.43

1 - P0 = 1 - 0.43 =0.57

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.52 -0.43 / [(0.43*0.57) / 80]

= 1.62

Test statistic = z =1.62

P(z > 1.62) = 1 - P(z < 1.62) = 1 - 0.9474

P-value = 0.0526

= 0.01

P-value > .

0.0526 >0.01

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that