Question

​Historically, the percentage of residents of a certain country who support laws has been 52​%. A recent poll of 987 people showed 531 in favor of laws. Assume the poll was given to a random sample of people. Test the claim that the proportion of those favoring stricter control has changed. Perform a hypothesis​ test, using a significance level of 0.05.

Answer 1

Solution :

Given that,

= 0.52

1 - = 0.48

n = 987

x = 531

Level of significance = = 0.05

Point estimate = sample proportion = = x / n = 0.538

This a two- tailed test.

The null and alternative hypothesis is,

Ho: p = 0.52

Ha: p 0.52

Test statistics

z = ( - ) / *(1-) / n

= ( 0.538 - 0.52) / (0.52*0.48) / 987

= 1.132

P-value = 2 * P(Z>z)

= 2*(1 - P(Z <z ))

= 2 * (1- P(Z < 1.132))

= 2 * 0.1288

= 0.2576

The p-value is p = 0.2576, and since p = 0.2576 > 0.05, it is concluded that fail to reject thenull hypothesis.

Conclusion:

It is concluded that fail to reject thenull hypothesis H0. Therefore, there is no enough evidence to claim that the populationproportion of those favoring stricter control has changed, at the α = 0.05 significance level.