Question

A data analytics firm hired by a Republican candidate running for political office wants to test whether its practices were successful in increasing voter turnout among registered Republicans. The firm collected data in a random selection of cities before the candidate ran for office and then after the election. Find the test statistic and the number of degrees of freedom for an appropriate hypothesis test using the data set below. Let the difference d for each city be computed as d=after−before. Assume that the populations are normally distributed. Round the test statistic to three decimal places.

Answer 1

Answer:

The practices were successful in increasing voter turnout among registered Republicans.

Step-by-step explanation:

The missing data is attached below.

The dependent t-test (also known as the paired t-test or paired samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.

In this case a paired t-test is used to determine whether the practices were successful in increasing voter turnout among registered Republicans.

The hypothesis for the test can be defined as follows:

H₀: The practices were not successful in increasing voter turnout among registered Republicans, i.e. d ≤ 0.

Hₐ: The practices were successful in increasing voter turnout among registered Republicans, i.e. d > 0.

Use Excel to perform the paired t-test.

Go to Data → Data Analysis → t-Test: Paired Two Sample for Means

A dialog box will open.

Select the variables.

Set the Hypothesized mean difference as 0.

Press OK.

The output is attached below.

The test statistic value is, t = 5.409.

The degrees of freedom is, df = 9.

The p-value for he one-tailed test is, p-value = 0.00021.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

The p-value of the test is very small for all the commonly used significance level. The null hypothesis will be rejected.

Thus, concluding that the practices were successful in increasing voter turnout among registered Republicans.