In: Statistics and Probability
The average American sees 15 movies per year. Amy believes that UCI students are different from the average American regarding movies. She gets a sample of four UCI students and asks them how many movies they see per year. They answer 2, 14, 2, 10. Do a t-test to see if Amy’s belief is true. Please calculate the t-statistic for this data. State the critical value, and come to a conclusion about Amy’s belief. Let α = .05. Make it a two-tailed test. Assume that it is okay to do a t-test.
We would be using the following table to make the required computations here:
X | (X - Mean(X))^2 |
2 | 25 |
14 | 49 |
2 | 25 |
10 | 9 |
108 |
The sample mean and sample standard deviation here is obtained as:
The t test statistic here is computed as:
Therefore -2.6667 is the required test statistic value here.
For 0.05 level of significance, and n - 1 = 3 degrees of
freedom, we have from the t distribution tables:
P( t3 < 3.182) = 0.975
Therefore, due to symmetry, we get here:
P( -3.182 < t3 < 3.182) = 0.95
Therefore - 3.182, 3.182 are critical values here.
As the critical value here is -3.182 < -2.6667, therefore the test statistic here lies in the non rejection region and we cannot reject the null hypothesis here. Therefore we have insufficient evidence here that the UCI students are different from the average American regarding movies