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

Answer: We will reject the null hypothesis and it is true that more than 50% of U.S tax returns were filled electronically last year.

Explanation:

Since we have given that

`H_0:p=\hat{p}\\\\H_a:\hat{p}>p`

Here, p = 0.5

n = 150

x = 86

so,
`\hat{p}=(x)/(n)=(86)/(150)=0.573`

So, test statistic value would be

`z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}\\\\z=\frac{0.573-0.50}{\sqrt{(0.5* 0.5)/(150)}}\\\\z=1.7963`

At 5% level of significance, z = 1.645

So, 1.645<1.7963

Hence, we will reject the null hypothesis.

P-value would be

`P(z>1.7963)\\\\=1-P(z\leq 1.7963)\\\\=1-0.9638\\\\=0.0362`

Hence, we will reject the null hypothesis and it is true that more than 50% of U.S tax returns were filled electronically last year.