8-4 Testing a Claim About a Standard Deviation or Variance 421 Alternative Method Used When Population Is Not Normal The methods of this section include two requirements: (1) The sample is a simple random sample; (2) the population is normally distributed. If sample data are not collected in a random manner, the methods of this section do not apply. If the sample appears to be from a population not having a normal distribution, we could use the confidence interval method of testing hypotheses, but obtain the confidence interval using bootstrap resampling, as described in Section 8-5. We could also use the resampling method of randomization. See Exercise 13 in Section 8-5. Hypothesis Test: Standard Deviation or Variance Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER Statdisk 1. Click Analysis in the top menu. 2. Select Hypothesis Testing from the dropdown menu and select Standard Deviation One Sample from the submenu. 3. Select the desired format for the Alternative Hypothesis, then enter the desired significance level and claimed standard deviation (from the null hypothesis). 4. Using Summary Statistics: Select the Use Summary Statistics tab and enter the sample size and sample standard deviation. Using sample data: Select the Use Data tab and select the desired data column. 5. Click Evaluate. StatCrunch 1. Click Stat in the top menu. 2. Select Variance Stats from the dropdown menu, then select One Sample from the submenu. 3. Using Summary Statistics: Select With Summary from the submenu and enter the sample variance and sample size. Using Sample Data: Select With Data from the submenu and select the desired data column. 4. Select Hypothesis test for s2 and for H0 enter the claimed value of the population variance. For HA select the format used for the alternative hypothesis. 5. Click Compute! Minitab 1. Click Stat in the top menu. 2. Select Basic Statistics from the dropdown menu and select 1 Variance from the submenu. 3. Using Summary Statistics: Select Sample standard deviation (or variance) from the dropdown menu and enter the sample size and sample standard deviation (or variance). Using Sample Data: Select One or more samples, each in a column from the dropdown menu and select the desired data column. 4. Check the Perform hypothesis test box and enter the standard deviation (or variance) used in the null hypothesis. 5. Click the Options button and enter the confidence level. (Enter 95.0 for a significance level of 0.05.) For Alternative hypothesis select the format used for the alternative hypothesis. 6. Click OK twice. TIP: Another procedure is to click on Assistant in the top menu, then select Hypothesis Tests and 1-Sample Standard Deviation. Complete the dialog box to get results, including P-value and other helpful information. TI-83, 83 84 Plus Calculator 8 us Ca cu ato 1. Download and install the Michael Lloyd programs S2TEST and ZZINEWT (available at www.TriolaStats. com) on your TI-83>84 Plus Calculator. 2. Press the N button, then select S2TEST from the menu and press [ twice. 3. Enter the population variance sx2, sample variance Sx2, and sample size n. Press [ after each entry. 4. For SIGMA2 select the desired format for the alternative hypothesis (3 for two-tailed test, * for left-tailed test, + for right-tailed test). 5. Press [ and the test statistic and the P-value will be provided. continued
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