Question

Now, suppose assuming the true fraction of voters is .65, the estimated standard deviation of X is given as 6.65. Suppose you find that 115 people actually voted yes in the random sample of 200. Conduct hypothesis testing using p value approach at 5% significance level to determine the validity of Candidate A’s claim that he was at least supported by 65% of the voters. (Make sure you show the steps of hypothesis testing)

Answer 1

reject H0 ; conclude that there is significant evidence to conclude that candidate A is supported by less than 65% voters

Explanation:

x = 115

n = 200

Phat = x / n = 115 / 200 = 0.575

H0 : P0 ≥ 0.65

H1 : P0 < 0.65

TEST STATISTIC :

Phat - P0 ÷ sqrt[(P0(1-P0))/n]

0.575 - 0.65 ÷ sqrt[(0.65(0.35))/200]

-0.075 ÷ 0.0337268

Test statistic -2.237

Pvalue :

P(Z < - 2.237) = 0.012643

α = 0.05

Pvalue < α

0.012643 < 0.05 ; We reject H0

We can conclude that there is significant evidence to conclude that candidate A is supported by less than 65% voters