Question

In a poll of 745 randomly selected adults, 591 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.

Answer 1

Answer:

The calculated value Z = 2.734 > 2.576 at 0.01 level of significance

Null hypothesis is rejected

The claim that 75% of adults say that it is morally wrong to report all income on tax returns.

Step-by-step explanation:

Step(i):-

Given random sample size 'n' = 745

Given In a poll of 745 randomly selected adults, 591 said that it is morally wrong to not report all income on tax returns

sample proportion

   $p^{-} = \frac{x}{n} = \frac{591}{745} = 0.7932$

Given Population proportion P = 0.75

                                           Q = 1-P

                                          Q = 1 - 0.75 = 0.25

Null Hypothesis :H₀: P=0.75

Alternative Hypothesis :H₁:P≠ 0.75

Step(ii):-

Test statistic

                          $Z = \frac{p^{-}-P }{\sqrt{\frac{P Q}{n} } }$

                          $Z = \frac{0.7932-0.75 }{\sqrt{\frac{0.75 X 0.25}{745} } }$

                          Z  = 2.734

Level of significance ∝ = 0.01

The critical value Z =2.576

The calculated value Z = 2.734 > 2.576 at 0.01 level of significance

Null hypothesis is rejected

The claim that 75% of adults say that it is morally wrong to report all income on tax returns.