Question

Suppose a poll is taken that shows that 795795 out of 15001500 randomly​ selected, independent people believe the rich should pay more taxes than they do. Test the hypothesis that a majority​ (more than​ 50%) believe the rich should pay more taxes than they do. Use a significance level of 0.05.

Answer 1

Yes. more than 50% is true.

Explanation:

Given that a poll is taken that shows that 795 out of 1500 randomly​ selected, independent people believe the rich should pay more taxes than they do.

Sample proportion p =
`(795)/(1500) =0.53`

Sample size n = 1500

Hypotheses would be

`H_0: p = 0.50\\H_a: p >0.50`

(Right tailed test at 5% significance level)

Std error of proportion =
`\sqrt{(P(1-P))/(n) } =\sqrt{(0.5(1-0.5))/(1500) } \\=0.0129`

Proportion difference = p-P =
`0.53-0.5=0.03`

Test statistic= p diff/std error =
`(0.03)/(0.0129) \\=2.33`

p value <0.05

Hence reject null hypothesis

There is significant difference in the two proportions and hence a majority​ (more than​ 50%) believe the rich should pay more taxes than they do is supported by statistical evidence.