Question 915:

Asked on December 6, 2011

Tags: Confidence Intervals , 1-sample t-test

1

Answer:

No answer provided yet.We can create a confidence interval around a sample to test a hypothesis about whether a population mean is a specific value. In this question it appears the population mean is missing, but I can assume from the data in might be 50.

To create the confidence interval we first compute the standard error of the mean (SE) by dividing the standard deviation by the square root of the sample size:

3/SQRT(20) = .671

Next we compute the margin of error by multiplying the SE times a t-critical value for a 95% level of confidence. Using a t-table or the Excel function =TINV(.05, 20-1) we get the critical value of 2.09. Multiplying this times the SE we get the margin of error of 1.404

Now we add and subtract this margin of error to the sample mean and get a 95% confidence interval of 47.596 to 50.404. Because the confidence interval DOES contain 50, we don't have enough evidence to conclude that the population mean is different than 50.

To run the hypothesis test we can conduct a 1-sample t-test using the same data. The test statistic is the difference between the sample mean and the SE we calculated in the last step. The test statistic is : -1/.671 = -1.49.

Looking up this value in a t-table or using the Excel function =TDIST(1.49,19,2) we get a p-value of .152. Because the p-value is greater than our alpha we fail to reject the Null Hypothesis.  We come to the same conclusion as we did with the confidence interval--we assume the population mean is 50.