Question

A poll of 1,068 adult Americans reveals that 48% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 level of significance, test the claim that at least half of all voters prefer the Democrat.

State the decision.

Answer 1

Solution :

This hypothesis test is a one tailed test .

The null and alternative hypothesis is

H₀ : p = 0.5

H_a : p < 0.5

= 0.48

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.48 - 0.5/ [(0.48 * 0.52) / 1068]

= -1.307

P-value =0.0956

= 0.05

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that   he claim that at least half of all voters prefer the Democrat.