Question 895:

Asked on July 19, 2011

Tags: 1-sample t-test , test statistic

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1. Q895_1_q895-1-sample-t.xls

For this question we need to test the hypothesis that the population mean is equal to 100. 

There are a few ways we can answer this question, I'll use the most popular and precise way.

We can conduct a 1-sample t-test and test to see if the sample data we are given is likely to have come from a population whose mean is 100.  The question only asks for the test statistic, which is the same for both a 1-sample t-test and 1-sample z-test.

The n represents the sample size
The s represents the sample standard deviation
The x (usually x-bar) is the sample mean.

Those are the 3 ingredients we need to conduct a 1-sample t-test.   The test statistic for a 1-sample t-test is the difference between the sample mean and the test mean divided by the standard error of the mean (SEM):

t (stat) = Difference / SEM

The SEM is the sample standard deviation divided by the square root of the sample size : 12/SQRT(36) = 12/6 = 2.
The difference between the sample mean and test mean is 96-100 = -4.
So the test statistic is then -4/2 = -2.