Question

Based on the $P$-value in Exercise 31, which of the following would be the most

appropriate conclusion?

a. Because the P-value is large, we reject $H_0$. We have convincing evidence that more than $50\%$of city residents support the tax increase.

b. Because the $P$-value is large, we fail to reject $H_0$. We have convincing evidence that more than $50\%$of city residents support the tax increase.

c. Because the $P$-value is large, we reject $H_0$. We have convincing evidence that at most $50\%$of city residents support the tax increase.

d. Because the $P$-value is large, we fail to reject $H_0$. We have convincing evidence that at most $50\%$of city residents support the tax increase.

e. Because the $P$-value is large, we fail to reject $H_0$. We do not have convincing

evidence that more than $50\%$of city residents support the tax increase.

Short answer

Option (e) is correct.

Step-by-step solution

Given Information

It is given that $H_0:p=0.50$

$H_1:p>0.50$

$P=0.18$

$p$refers to proportion of all cities that helps$1\%$increase in sales tax to fund repair of roads.

Explanation

We know that if $p\mathrm{level}<\mathrm{\alpha }$, null hypothesis is rejected.

Generally $\alpha =0.01,0.05,0.10$, $P$value is larger than all these three levels.

Hence, we fail to reject null hypothesis and there will be no convincing evidence that alternate hypothesis is true.

So, there is not enough convincing proof majority of residents helps to increase in tax.

Option (e) is correct.