Question

The polls just closed Maryland and your candidate wants to claim victory. She calms more than half of the people voted for her. New exit polls indicate 235 of the 500 voters voted for the candidate. Does the new poll support her claim at a 95% confidence level that at least 51% of the voters voted her? (Ho: p >= 0.51) What is the test statistic Round your answer to 2 decimal places)

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.51

Ha : p > 0.51

n =500

x =235

= x / n = 235 / 500 = 0.47

P0 = 0.51

1 - P0 = 1-0.51=0.49

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.47 - 0.51 / [(0.51*0.49) / 500]

= -1.791 -

Test statistic = z = -1.79

P(z > -1.79 ) = 1 - P(z < -1.79 ) = 1- 0.0367

P-value = 0.9633

= 0.05

P-value >

0.9633 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that