Question

Your political party received 40% of the votes in the last election. You want to see if

your level of support has changed since the election. You sample 235 voters, and find that 107 would vote for you if an election were held today. Perform a hypothesis test at the 0.01 level to test if your support has changed.

Answer 1

Solution :

Given that,

= 0.40

1 - = 0.60

n = 235

x = 107

Level of significance = = 0.01

Point estimate = sample proportion = = x / n = 0.455

This a two- tailed test.

The null and alternative hypothesis is,

Ho: p = 0.40

Ha: p 0.40

Test statistics

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

= ( 0.40 - 0.455) / (0.40*0.60) /235

= -1.72

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

= 2 * P(Z < -1.72 )

= 2 * 0.0427

= 0.0854

The p-value is p = 0.0854, and since p = 0.0854 > 0.01, it is concluded that the null hypothesis is fail to rejected.

Therefore there is not sufficient evidence to claim that to test if your support has changed, at 0.01 level of significance.