Suppose that a survey of 500 randomly selected registered voters are asked whether they voted in
the last presidential election and that 49% said that they had. We wish to test the claim at the a = 0.05 level of
significance that more than 50% of registered voters voted in the last presidential election.
Null hypothesis: "H_0:p=0.5"
Alternative hypothesis: "H_a:p>0.5"
The test statistic is found using n=500 and "\\^p=0.49" . We get
"z=\\frac{0.49-0.5}{\\sqrt{\\frac{0.5*0.5}{500}}}=-0.4472."
At "\\alpha=0.05" the critical value "z" will be "z=1.645" (using t-table).
The rejection region for this right-tailed test is "R = \\{z: z > 1.645\\}."
Our test statistic does not fall within the rejection region (it is less than 1.645), so we cannot reject the null hypothesis.
Comments
Leave a comment