EXAMPLE 20 test for comparing two population standard deviations: Critical-value method

Table 18 shows independent samples from Google and Apple stock prices from July 2014 together with the sample sizes and sample standard deviations. Test, using the critical-value method, whether the standard deviation of Google stock prices is greater than the standard deviation of Apple stock prices .

Table 10.62: Table 18 Independent random samples of stock prices, July 2014
Google Apple
574.79 590.76 583.04 593.06 580.82
599.02 579.55 587.78		 93.52 94.03 95.39 96.45 95.60 99.02
97.03
Table 10.62: Source: www.marketwatch.com/tools/quotes/historical.asp.

Solution

The normal probability plots in Figures 22a and 22b show acceptable normality for both samples. We may, therefore, proceed with the test for comparing population standard deviations.

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Figure 10.22: FIGURE 22a Normal probability plot of Google stock prices.
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Figure 10.23: FIGURE 22b Normal probability plot of Apple stock prices.

  • Step 1 State the hypotheses. We are testing whether Google's stock prices are more variable than those of Apple. Thus, because Google represents population 1, we have the following hypotheses for our test:

    where represents the standard deviation of Google stock prices and represents the standard deviation of Apple stock prices. Use level of significance .

  • Step 2 Find the critical value and state the rejection rule. We have and . From Table 17 and Appendix Table F, our critical value is the -value with area to the right of it:

    Our rejection rule is, therefore, from Table 17: Reject if .

    623

  • Step 3 Find

    follows an distribution with and .

  • Step 4 State the conclusion and the interpretation. Because is greater than , we reject . There is evidence that the variability in Google stock prices is greater than the variability in Apple stock prices.

NOW YOU CAN DO

Exercises 21–26.