Question 848:

Asked on March 5, 2010

Tags: Paired t-test

1

Answer:

No answer provided yet.Since we have two sets of data for the same family we can use the paired t-test, also called the 2-sample t-test on dependent means. The Null Hypothesis is that the mean difference between insurance companies is 0. The alternative hypothesis is that the difference between rates is greater or less than 0. We will reject the Null Hypothesis if we obtain a p-value less than the alpha cut-off of .05.

The test statistics t* is found first by subtracting each insurance price per family to get a difference value. We then take the average of all the difference values and divide by the standard error of the mean difference (SE). The average of the difference values is -246.3. The SE is found as the standard deviation of the difference values divided by the square root of the sample size = 546.9/SQRT(15) = 141.224. So the test statistic t* is -246.3/141.224 = -1.744. We lookup this t-value in a t-table using 14 degrees of freedom and get the 2-tailed p-value of  .103. You can also use the excel function = TDIST(1.744,14,2).

Since the p-value is greater than the cutoff of .10 we fail to reject the null hypothesis and conclude that the difference between the rates is not different than 0. In other words, there is likely not a difference in the rates between insurance companies.