Question

4. In a sample of 100 registered voters, 54 said that they might vote for Candidate A. Test
the research hypothesis that Candidate A’s approval rating is greater than 50% against the
null hypothesis that it is 50%. Give a p-value for the preceding problem ??

Show work please

Answer 1

H0: p <= 0.50

Ha: p > 0.50 (Right tailed)

Sample proportion = 54 / 100 = 0.54

Test statistics

z = - p / sqrt( p ( 1 - p) / n)

= 0.54 - 0.50 / sqrt( 0.50 * 0.50 / 100)

= 0.8

This is test statistics value.

p-value = P (Z > z)

= P (Z > 0.8)

= 1 - P( Z < 0.8)

= 1 - 0.7881

= 0.2119

Since p-value > 0.05 significance level, we do not have sufficient evidence to reject H0.

We conclude at 0.05 significant level that we fail to support the claim.