Question

Previously, 10.5% of workers had a travel time to work of more than 60 minutes. An urban economist believes that the percentage has increased since then. She randomly selects 75 workers and finds that 14 of them have a travel time to work more than 60 minutes. Test the economist’s belief at the 0.1 level of significance. Find the P-value and make a conclusion about the null.

Answer 1

Given that, n = 75 and x = 14

=> sample proportion = 14/75 = 0.1867

The null and alternative hypotheses are,

H0 : p = 0.105

Ha : p > 0.105

This hypothesis test is a right-tailed test.

Test statistic is,

=> Test statistic = Z = 2.31

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

P-value = P(Z > 2.31) = 1 - P(Z < 2.31) = 1 - 0.9896 = 0.0104

=> P-value = 0.0104

Since, p-value is less than 0.1 level of significance, we reject the null hypothesis (H0).

Conclusion : There is sufficient evidence to conclude that the percentage has increased since then.