Question

In a 2016 survey of 957 registered voters, 321 people believe that the threats from climate change are overstated. In a 2018 survey of 962 registered voters, 371 of those surveyed also shared this view. Perform a hypothesis test to test the claim that the proportion of registered voters who believe that the threats from climate change are overstated has increased.

Answer 1

To test if the proportion of registered voters who believe the threats from climate change are overstated has increased, perform a hypothesis test using the z-test for proportions on the 2016 and 2018 survey data sets.

Step-by-step explanation:

To test the claim that the proportion of registered voters who believe the threats from climate change are overstated has increased, we can perform a hypothesis test on the two survey data sets from 2016 and 2018.

Step 1: Define the null and alternative hypothesis.
Null hypothesis (H0): The proportion of registered voters who believe the threats from climate change are overstated has not increased.
Alternative hypothesis (Ha): The proportion of registered voters who believe the threats from climate change are overstated has increased.

Step 2: Calculate the test statistic.
For this hypothesis test, we will use the z-test for proportions. The test statistic is calculated using the formula: z = (p - p0) / sqrt((p0 * (1 - p0)) / n), where p is the sample proportion, p0 is the hypothesized proportion, and n is the sample size. In this case, the sample proportions are p1 = 321/957 and p2 = 371/962.
Calculate the difference in proportions: p2 - p1. Calculate the standard error: sqrt((p1 * (1 - p1)) / n1 + (p2 * (1 - p2)) / n2). Finally, calculate the test statistic: z = (p2 - p1) / SE.

Step 3: Determine the critical value and reject or fail to reject the null hypothesis.
Using a significance level of 0.05, a critical value of z = 1.96 is used for a two-tailed test. If the test statistic is greater than the critical value or less than the negative of the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Step 4: Interpret the results.
If the null hypothesis is rejected, we can conclude that there is evidence to suggest that the proportion of registered voters who believe the threats from climate change are overstated has increased. If the null hypothesis is not rejected, we do not have enough evidence to support the claim that the proportion has increased.