Statistics
posted by Stanley on .
It is believed that at least 60% of voters from a certain region in Canada favor the free trade agreement (FTA). A recent poll indicated that out of 400 randomly selected individuals, 250 favored the FTA. If we wished to perform a test to determine whether the proportion of those favoring the FTA is greater than 60%, at the 5% level of significance, we would:
Fail to reject H0 since the calculated value of the test statistic is 1.033 which is less than 1.645.
Fail to reject H0 since the calculated value of the test statistic is 1.033 which is less than 1.96.
Fail to reject H0 since the calculated value of the test statistic is 1.0204 which is less than 1.96.
Fail to reject H0 since the calculated value of the test statistic is 1.0204 which is less than 1.645.
Not need to test since everyone knows that FTA is good.

A seed company claims that 80% of the seeds of a certain variety of tomato will germinate if sown under normal growing conditions. A government inspector is interested in whether or not the proportion of seeds germinating is living up to the company's claim. He randomly selects a sample of 200 seeds from a large shipment and tests the sample for percentage germination. If 155 of the 200 seeds germinate, then the calculated value of the test statistic used to test the hypothesis of interest is:
 .847
.884
.897
.825
.858

Using a formula for a binomial proportion onesample ztest with your data included, we have:
z = .625  .60 >test value (250/400 = .625) minus population value (.60)
divided by
√[(.60)(.40)/400]
Calculating, z = 1.02
Critical value = 1.645 (onetailed)

Test statistic for your second problem can be calculated the same way:
z = .775  .80 >test value (155/200 = .775) minus population value (.80)
divided by
√[(.80)(.20)/200]
Calculating, z = 0.884