## Question 833:

Asked on December 9, 2009

Tags:
1-sample t-test ,
Hypothesis Test

1

## Answer:

No answer provided yet.For this question we want to know if there is evidence that a sample mean is different than a particular population mean. We'll use the 5-step hypothesis testing procedure and use the 1-sample t test.

- The Null hypothesis is that there is no difference between the salaries of Political Science students and the average American. The alternate hypothesis is that there is a difference in average salaries.
- We will conduct a 1-sample t-test against the test mean of $36,345.45 and reject the Null Hypothesis if the p-value is less than the alpha value of .05.
- In conducting a 1-sample t-test the test-statistic t is found using the following steps:
- Find the difference in the sample mean and test mean = 36,878.25-36,345.45 = $532.80
- Divide this difference by the standard error of the mean (SEM). The SEM is found as the standard deviation divided by the square root of the sample size = 400/SQRT(25) = 400/5 = 80.
- The test statistic t = 532.8/80 = 6.66.
- We lookup the t-statistic using a t-table on n-1 degrees of freedom (24) and we get the 2-sided p-value of less than .001.

- Since the p-value is far less than our alpha cut-off value of .05 there is sufficient evidence for us to reject the Null Hypothesis.
- We conclude that Political Science students make a different salary than the average American.

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