Determining whether an individual's political affliation affects his or her overall satisfaction with the economy.

For this assignment, use only subjects that declared themselves as Republicans or
Democrats and leave out any subjects who declared themselves as Independent or Undecided. Analyze any potential differences by conducting the appropriate type of t-test. This is the data

Subject 1 Republican

Satisfaction with Economy 9 Satisfaction with job 10

Subject 2 Republican
Satisfaction with Economy 7
Satisfaction with job 9

Subject 3 Democrat
Satisfaction with Economy 6
Satisfaction with job 8

Subject 4 Democrat
Satisfaction with Economy 10
Satisfaction with job 5

To analyze whether an individual's political affiliation affects their overall satisfaction with the economy, we need to perform a t-test on the data provided. We will compare the mean satisfaction with the economy for Republicans and Democrats to determine if there is a significant difference between the two groups.

First, let's calculate the mean satisfaction with the economy for each group:

Republicans:
(9 + 7) / 2 = 8

Democrats:
(6 + 10) / 2 = 8

Next, let's calculate the standard deviation for each group:

Republicans:
Step 1: Calculate the squared deviation for each observation:
(9 - 8)^2 = 1
(7 - 8)^2 = 1

Step 2: Calculate the sum of squared deviations:
1 + 1 = 2

Step 3: Calculate the variance:
2 / 2 = 1

Step 4: Calculate the standard deviation:
sqrt(1) = 1

Democrats:
Step 1: Calculate the squared deviation for each observation:
(6 - 8)^2 = 4
(10 - 8)^2 = 4

Step 2: Calculate the sum of squared deviations:
4 + 4 = 8

Step 3: Calculate the variance:
8 / 2 = 4

Step 4: Calculate the standard deviation:
sqrt(4) = 2

Now, let's perform the t-test to determine if there is a significant difference between the two groups:

Step 1: Calculate the t-statistic:
t = (mean of Republicans - mean of Democrats) / sqrt[(variance of Republicans / number of Republicans) + (variance of Democrats / number of Democrats)]

t = (8 - 8) / sqrt[(1 / 2) + (4 / 2)]
t = 0 / sqrt[(0.5) + (2)]
t = 0 / sqrt(2.5)
t = 0

Step 2: Determine the degrees of freedom:
degrees of freedom = number of Republicans + number of Democrats - 2 = 2 + 2 - 2 = 2

Step 3: Look up the critical t-value for the desired significance level (e.g., α = 0.05) with the corresponding degrees of freedom (2).

With 2 degrees of freedom, the critical t-value for α = 0.05 is approximately 4.303.

Step 4: Compare the calculated t-value to the critical t-value:

Since the calculated t-value (0) is less than the critical t-value (4.303), we fail to reject the null hypothesis. This means that there is not enough evidence to suggest a significant difference in overall satisfaction with the economy between Republicans and Democrats.

In conclusion, based on the t-test analysis, there is no statistical evidence to support the claim that political affiliation affects overall satisfaction with the economy.