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.
Fail to reject H0 since the calculated value of the test statistic is 1.033 which is less than 1.96.
To determine whether the proportion of voters favoring the free trade agreement (FTA) is greater than 60%, we can perform a hypothesis test using a significance level of 5%.
In this case, our null hypothesis (H0) would be that the proportion of voters favoring the FTA is equal to or less than 60%, while the alternative hypothesis (Ha) would be that the proportion is greater than 60%.
To calculate the test statistic, we can use the formula for a test of proportions:
z = (p - P) / √((P(1-P)) / n)
Where:
- p is the proportion from the sample (250/400 = 0.625),
- P is the assumed population proportion under the null hypothesis (0.60),
- n is the sample size (400).
Plugging in these values, we get:
z = (0.625 - 0.60) / √((0.60 * (1-0.60)) / 400)
= 0.025 / √((0.60 * 0.40) / 400)
= 0.025 / √(0.24 / 400)
= 0.025 / √0.0006
≈ 1.033
The calculated value of the test statistic is approximately 1.033.
Now, to determine whether we should reject or fail to reject the null hypothesis, we need to compare the calculated test statistic with the critical value associated with our chosen significance level.
Since we have a right-tailed test (the alternative hypothesis is that the proportion is greater than 60%), the critical value for a 5% significance level is 1.645.
Comparing the calculated test statistic (1.033) with the critical value (1.645), we see that the calculated test statistic is less than the critical value.
So, the correct answer is: Fail to reject H0 since the calculated value of the test statistic is 1.033 which is less than 1.645.