Question

State your decision to the significance test in terms of the null hypothesis.According to a recent poll, the percentage of Americans who would vote for the incumbent president is 53%. If a random sample of 100 people in New York results in 45% who would vote for the incumbent, test the claim that the percentage of people in New York who would vote for the incumbent president is different from 53%. Use the following results and a 0.10 significance level to state your decision about H0.

H0 : p=0.53
H1 : p≠0.53
Test statistic: z = -1.60 p-value = 0.1090

Answer 1

To test the claim that the percentage of people in New York who would vote for the incumbent president is different from 53%, set up the null and alternative hypotheses. This is a two-tailed test with a p-value of 0.1090. At the 1 percent significance level, fail to reject the null hypothesis.

Step-by-step explanation:

To test the claim that the percentage of people in New York who would vote for the incumbent president is different from 53%, we can set up the null and alternative hypotheses as follows:

Null hypothesis (H0): p = 0.53

Alternative hypothesis (H1): p ≠ 0.53

Since the alternative hypothesis (H1) is two-tailed, this is a two-tailed test. The p-value is the probability of observing a test statistic as extreme as the one observed or more extreme, given that the null hypothesis is true. In this case, the p-value is 0.1090. At the 1 percent significance level, we would compare the p-value to the significance level. Since the p-value (0.1090) is greater than the significance level (0.01), we fail to reject the null hypothesis.