Bluman A.G. Elementary Statistics- A Step By Step Approach

Section 8–5 x 2 Test for a Variance or Standard Deviation 449Figure 8–35Critical Value forExample 8–240.050.9512.338Step 3Compute the test value.x 2 n 1s2s 223 1198225 19.36Step 4Make the decision. Since the test value 19.36 falls in the noncritical region, asshown in Figure 8–36, the decision is to not reject the null hypothesis.Figure 8–36Critical and Test Valuesfor Example 8–240.050.9512.338 19.36Step 5Summarize the results. There is not enough evidence to support the claim thatthe variation in test scores of the instructor’s students is less than the variationin scores of the population.Example 8–25Outpatient SurgeryA hospital administrator believes that the standard deviation of the number ofpeople using outpatient surgery per day is greater than 8. A random sample of15 days is selected. The data are shown. At a 0.10, is there enough evidence tosupport the administrator’s claim? Assume the variable is normally distributed.Solution25 30 5 15 1842 16 9 10 1212 38 8 14 27Step 1State the hypotheses and identify the claim.H 0 : s 8 and H 1 : s 8 (claim)Since the standard deviation is given, it should be squared to get the variance.Step 2 Find the critical value. Since this test is right-tailed with d.f. of 15 1 14and a 0.10, the critical value is 21.064.Step 3Compute the test value. Since raw data are given, the standard deviation of thesample must be found by using the formula in Chapter 3 or your calculator. Itis s 11.2.x 2 n 1s2s 215 111.2264 27.448–51