Question

A Democratic candidate stated that 42% of the voters in Illinois are Republicans. In a sample of 500 registered voters, 225 indicated they are Republicans. Set up the null and alternative hypotheses that can be used to test the candidate’s statement. Use a 10% level of significance to test the candidate’s statement using both the critical value and p-value approaches. Do your tests support the candidate’s statement or not? Explain.

Answer 1

H0: p = 0.42

Ha: p 0.42

Sample proportion = 225 / 500 = 0.45

Test statistics

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

= ( 0.45 - 0.42) / sqrt [ 0.42 ( 1 - 0.42) / 500 ]

= 1.36

Critical values at 0.10 significance level = -1.645 , 1.645

Since test statistics falls in non-rejection region, fail to reject H0.

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

= 2 * P( Z > 1.36)

= 2 * 0.0869

= 0.1738

Since p-value > 0.10 significance level, fail to reject H0.

We conclude that we support the candidate’s statement