Question

Historically 40% of voters are Republicans. A simple random sample of 320 registered voters find that 142 are registered Republicans. Does this indicate that there are now more than 40% registered Republicans?

Answer 1

Solution :

This hypothesis test is a one tailed test .

The null and alternative hypothesis is

H₀ : p = 0.40

H_a : p > 0.40

= x / n = 142 / 320 = 0.44375

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.44375 - 0.40 / [(0.40 * .60) /320 ]

= 1.598

P-value = 0.0551

At , = 0.05

P-value >

Fail to reject the null hypothesis .

There is sufficient evidence to suggest that there are now more than 40% registered Republicans .