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 0.05 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.

a. Identify the correct null and alternative hypotheses.

b. The test statistic is z = __

c. The​ P-value is __

d. Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim:

__ H0. There ___ sufficient evidence to warrant rejection of the claim that 70% of adults say that it is morally wrong not to report all income on tax returns.

Answer 1

Solution: Here, the given information are

n=745, x=586, p0=0.75,  =0.05

=x/n = 586/745 = 0.7866

a) Hypothesis

Null hypothesis : p0=0.75 that means 75% of adults say that it is morally wrong to report all income in tax returns.

Alternative hypothesis: p0 0.75, 75% of adults say that it is morally wrong not to report all income on tax returns.

b) The test statistic is

z=

=

z = 2.306

c) P-value = 2*(1-P(z)) ---------- For two sided

= 2*(1-(2.31)) ------------round up

= 2*(1-0.9896))----------------from z table.

=2*0.0104 =0.0208

P-value=0.0208

d) Reject H0. There is 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.