Question 907:

Asked on December 3, 2011

Tags: 1-sample t-test

1

Answer:

No answer provided yet.We will use a 1-sample t-test here to test the hypothesis that the population mean is equal to 50.

The test statistic is found as the difference between the sample and test mean (which is 49-50) divided by the standard error of the mean (SEM). The SEM is the standard deviation divided by the square root of the sample size : 3/SQRT(20) = .671 

So the test statistic is -1/.671 = -1.49

To find the significance of this test statistic we need to use a t-table or use the Excel function = TDIST(1.49,19, 2) where the parameters are the test statistic, the degrees of freedom (20-1) and 2 tails for a 2-sided test of significance.

We get a 2-tailed p-value of .1524 which is GREATER than the alpha value of .05. We then fail to reject the null hypothesis. We conclude that the population mean is equal to 50.