In the 2004 Presidential election, one of the hotly contested states was Ohio. O
ID: 3041063 • Letter: I
Question
In the 2004 Presidential election, one of the hotly contested states was Ohio. Oftentimes, exit polls are used to predict which candidate will carry that state (i.e. get a majority of the votes in that state). In 2004, there were 2020 Ohio residents that participated in an exit poll. Of those polled, 1030 said that they voted for Bush.
a. With this information, could one conclude that Bush would carry Ohio at the 0.05 significance level using the Coin Tossing applet? State the null model and report the p-value?
b. Now perform a traditional hypothesis test (by hand) to see that Bush would carry Ohio at the 0.05 significance level?
Context:
Conditions:
Calculations:
Conclusion:
c. Use Minitab to confirm the test statistic and the p-value.
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P < 0.50
Alternative hypothesis: P > 0.50
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).
= sqrt[ P * ( 1 - P ) / n ]
= 0.011125
z = (p - P) /
z = 0.89
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.
Since we have a one-tailed test, the P-value is the probability that the z-score is greater than 0.89.
Thus, the P-value = 0.1867.
Interpret results. Since the P-value (0.1867) is greater than the significance level (0.05), we have to accept the null hypothesis.
From the above test we do not have sufficeint evidence in the favor of the claim that Bush would carry Ohio at the 0.05 significance level.