Question

Suppose that a campaign manager claims that the percent of registered voters who prefer his candidate is 60 percent. A pollster conducts a random survey of 500 registered voters to test the campaign manager's claim and finds that 58 percent of the sample of registered voters preferred the campaign manager's candidate. Perform the test of hypothesis at the α = 0.10 level of significance.

Answer 1

Null hypothesis $H_0:p=0.6.$

Alternative hypothesis $H_a:p\ne 0.6.$

Test statistic: $z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.58-0.6}{\sqrt{\frac{0.6(1-0.6)}{500}}}=-0.91.$

P-value: $p=0.3628.$

Since P-value is greater than 0.10, fail to reject the null hypothesis.