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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.

Respuesta :

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.

Step-by-step explanation:

Since we have given that

[tex]H_0:p=\hat{p}\\\\H_a:\hat{p}>p[/tex]

Here, p = 0.5

n = 150

x = 86

so, [tex]\hat{p}=\dfrac{x}{n}=\dfrac{86}{150}=0.573[/tex]

So, test statistic value would be

[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.573-0.50}{\sqrt{\dfrac{0.5\times 0.5}{150}}}\\\\z=1.7963[/tex]

At 5% level of significance, z = 1.645

So, 1.645<1.7963

Hence, we will reject the null hypothesis.

P-value would be

[tex]P(z>1.7963)\\\\=1-P(z\leq 1.7963)\\\\=1-0.9638\\\\=0.0362[/tex]

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.

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