Question

A government Bureau claims that more than 50% of U.S. tax returns were filed electronically last year. A random sample of 150 tax returns for last year contained 86 that were filed electronically. Test the Bureau's claim at a 5% level of significance. What is your conclusion? Report the p-value for this test.

Answer 1

Solution:

H₀: p = 0.50

H_a: p > 0.50

Let   be the sample proportion.

= x/n = 86/150 = 0.5733

The test statistic z is

z =   

=  (0.5733 - 0.50)/[0.50*(1 - 0.50)/150]

= 1.795

The test statistic z = 1.795

> sign in Ha indicates that right tailed test

p value = P(Z > 1.795) = 1 - P(Z < 1.795) = 1 - 0.9637 = 0.0363

p value = 0.0363

Given , = 5% = 0.05

p value is less than

Reject H₀ at 5% level of significance.

Conclusion:

There is sufficient evidence to support government Bureau's claim that more than 50% of U.S. tax returns were filed electronically last year.