Question

In a recent poll of 755 randomly selected adults, 587 said that it is morally wrong to not report all income on tax returns. Use a 0.05 significance level to test claim that 75% of adults say that it is morally wrong to not report all income on tax returns. Identify the null hypothesis, test statistic, P-value, and final conclusion that addresses the original claim. Use the normal distribution as an approximation of the binomial distribution.

Answer 1

Claim : To test whether that the 75% of adults say that it is morally wrong to not report all income on tax returns

Hypothesis :

Two tailed test

Let x = number of individuals who  morally wrong to not report all income on tax returns = 587

Given that

sample size = n = 755

Proportion of individuals who  morally wrong to not report all income on tax returns = p = 0.75

Here n*p and n * q both are greater than 5

Therefor  normal distribution as an approximation of the binomial distribution is approporiate to use

Therefor, sample proportion is

Test statistics :

..............( test statistics)

Pvalue =

...............( From Z table)

     

Decision Rule : we fail to Reject Ho

Concusion : There is INSUFFICIENT evidence to conclude that the 75% of adults say that it is morally wrong to not report all income on tax returns​.