Question

In the past, the proportion of nc voters who plan to support candidate a has been 20%. a researcher wishes to test, at the 7% level of significance whether the proportion is greater now. she takes a random sample of 1600 voters in nc (based on active voting history and a survey by mail) and finds that 315 nc voters support candidate a. test the researcher's claim. state the null and alternative hypothesis

Answer 1

The null and alternative hypotheses for the study are H0: p = 0.20 and HA: p > 0.20, respectively. One calculates the test statistic using the sample proportion, hypothesized population proportion, and sample size to carry out the hypothesis test.

Step-by-step explanation:

The research question is to test at the 7% level of significance whether the proportion of North Carolina (NC) voters who plan to support candidate A is greater now compared to the past proportion, which was 20%. Given a sample of 1600 voters, 315 were found to support candidate A.

Step 1: Define the Null and Alternative Hypothesis

The null hypothesis (H0) and the alternative hypothesis (HA) are defined as follows:

1. H0: p = 0.20 - The proportion of NC voters supporting candidate A is 20%.
2. HA: p > 0.20 - The proportion of NC voters supporting candidate A is greater than 20%.

Step 2: Calculate the Test Statistic

The test statistic for a proportion is calculated using the formula:

z = (p' - p0) / sqrt(p0(1 - p0) / n)

where p' is the sample proportion (315/1600), p0 is the hypothesized population proportion (0.20), and n is the sample size (1600).