Question

Before the last presidential debates, 50% of registered votes indicated they were planning to vote for the incumbent president. In a recent poll of 1200 registered voters after the debates, 636 indicated they are planning to vote for the incumbent president. Has there been a significant increase in the proportion of registered voters who are planning to vote for the incumbent president?

1. State the null and alternative hypotheses to be tested.

2. Compute the test statistic.

   The null hypothesis is to be tested using α = 0.05. Determine the

   critical value(s) for this test.

4. What do you conclude?

5. Compute the p-value.

Answer 1

Solution:

Given in the question

Null hypothesis H0: p=0.5

Alternate hypothesis Ha: p>0.5

Sample proportion = (636/1200) = 0.53

Here we will use One sample proportion Z test

Test statistic can be calculated as

Test stat = (Sample proportion - p) /sqrt(p*(1-p)/n) = (0.53-0.50)/sqrt(0.5*(1-0.5)/1200) = (0.03)/0.0144 = 2.08

At alpha = 0.05, and this is right tailed and one tailed test

So from Z table we found critical value = 1.645

If test stat value is greater than 1.645 than reject the null hypothesis else do not reject the null hypothesis.

Here we can see that Test statistic value is greater than critical value. So we can reject the null hypothesis and we have significant evidence to support the claims I.e. proportion of registered voters who are planning to vote has increased.

At Z test stat = 2.08 and this is right tailed and one tailed test so p- value from Z table is 0.0188

So p- value = 0.0188