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Question 542:



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We can use the 2-sample test here to compare the two mean turn-over rates. The test-statistic is generated by subtracting the means and dividing by the standard deviation of the sample. We are NOT told to assume equal variances and the sample sizes are different and perhaps come from different populations. We need to generate the estimate of this standard deviation using the following procedure.

  1. First we generate a pooled standard deviation using the variance (squaring the standard deviation) since we're assuming there is a difference between variances.
    1. The variances are 26.01 and 44.89
    2. In assuming unequal variances we use the formula for the pooled standard deviation
      1. SQRT( (var1/n1) + (var2/n2) )
      2. SQRT( (26.01/32) + (44.89/49) ) = 1.3148 which is the pooled standard deviation
    3. The difference between the means is 34.9.-31.4= 3.5 making the test statistic = 3.5/1.3148= 2.66
    4. There  are 79 degrees of freedom (n1+n2-2).
    5. Looking up the p-value associated with this t-statistics and 79 degrees of freedom gets us a p-value of .009  We can also use the Excel function =TDIST(2.66,79,2), where the parameters are the t-statistics, degrees of freedom and 2 tailed test.
  2. The p-value of .009 is below our rejection criteria of .01 meaning we would reject the null hypothesis. This means we would say there is a significant difference in turnover rates between the two types of stocks.

Note: We had to make a call here on whether to assume equal or unequal variances. If we had assumed equal variances then we'd get a p-value of .014, and NOT reject the Null hypothesis. To me it is more logical to NOT assume that each of these stocks would have the same variances since they appear to come from populations with different amounts of variability.

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