Question

In a recent poll of 745 randomly selected​ adults, 586 said that it is morally wrong to not report all income on tax returns. Use a 0.01 significance level to test the claim that 75% of adults say that it is morally wrong to not report all income on tax returns. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method. Use the normal distribution as an approximation of the binomial distribution.

Identify the correct null and alternative hypotheses.

The test statistic is z=

The​ P-value is

Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim.▼Fail to reject/Reject H0. There▼is/is not sufficient evidence to warrant rejection of the claim that 75% of adults say that it is morally wrong not to report all income on tax returns.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.75

Ha : p 0.75

n = 745

x = 586

= x / n = 586 / 745 = 0.79

P0 = 0.75

1 - P0 = 1-0.75=0.25

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.79 - 0.75 / [(0.75*0.25) / 745 ]

= 2.30

Test statistic = z = 2.30

P(z > 2.30) = 1 - P(z < 2.30 ) = 1 - 0.9893

P-value = 2 * 0.0107 =0.0214

= 0.01

P-value >

0.0214 > 0.01

Fail to reject/Reject H0. There is not sufficient evidence to warrant rejection of the claim that 75% of adults say that it is morally wrong not to report all income on tax returns.