Question

In 2000, National data suggested that 26% of all U.S. businesses were owned by women. In 2009, a consulting firm surveyed a random sample of 700 U.S. businesses and found that 28% of them were owned by women. Is this evidence of an increase in the percentage of businesses that are owned by women in the U.S?

The hypotheses for this test are:

H 0: p = 0.26

H A: p > 0.26

Find the P-value for the test and, based on your P-value, what should be your decision for H 0.

Answer 1

Given that, sample size (n) = 700 and

sample proportion = 0.28

The null and alternative hypotheses are,

H0 : p = 0.26

HA : p > 0.26

This hypothesis test is a right-tailed test.

Test statistic is,

=> Test statistic = Z = 1.21 (rounded to two decimal places)

Using standard normal z-table we find the p-value,

p-value = P(Z > 1.21) = 1 - P(Z < 1.21) = 1 - 0.8869 = 0.1131

=> P-value = 0.1131

Since, p-value is greater than 0.05 level of significance, we fail to Reject H0.