Question 786:

Asked on July 27, 2009

Tags: 2-sample t-test

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1. Q786_1_q7862_samplet.xls

We can conduct a 2-sample t-test to determine if the difference in the mean length of telephone calls was reduced. We're told to use a right-tailed test, which means using only the 1-tailed probability instead of the 2-tailed probability.

Part a.
The Null hypothesis is that there is no difference in mean call lengths between months.
The alternative hypothesis is that the mean length is less in August than in July.

The sample sizes are not equal and the difference in standard deviations is greater than 2 so it's best to assume unequal variances (which is also what we're told to do). The test-statistic t* can be found by subtracting the difference between means and dividing by the standard error of the difference between the means. The attached file shows the calculations.

Part b.
The observed difference is 2.084 and the standard error of the difference is .789 generating a t-statistic of -2.6398 on 81 degrees of freedom. This generates a p-value of .00497. Since this is less than our alpha of .01 we reject the Null Hypothesis and conclude the mean length is less in august.

Part c.
Since we're dealing with call lengths there's a good chance that the distribution will be positively skewed due to some really long phone calls. Positive skew is a common attribute of cycle time data like phone call length.   When the data are not normally distributed and we're using a 1-tailed test, this will likely give us an inaccurate p-value. There is a chance there is more than the stated area (in this case .00497) under the right tail of the curve and so we should interpret the p-value with some caution.