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Chapter 7 , 7 376 EXAMPLE 7-3 Credit Union Assets The following data represent a random sample of the assets (In millions of dollars) of 30 credit unions in southwestern Pennsylvania. Assume the population standard deviation is 14.405. Find the 90%% confidence interval of the mean. 12.23 16.56 1.39 2.89 1.24 2.17 13.19 9.16 1.42 73.25 1.91 14.64 11.59 6.69 1.06 8.74 3.17 18.13 7.92 4.78 16.85 40.22 2.42 21.58 5.01 1.47 12.24 2.27 12.77 2.76 Source: Pittsburgh Post Gazette. SOLUTION Step 1 Find the mean for the data. Use the formula shown In Chapter 3 or your calculator. The mean .X = 11.091. Assume the standard deviation of the population is 14.405. Step 2 Find a/2. Since the 90% confidence interval is to be used, a - 1 - 0.90 = 0.10, and 0.10 2 0.05 Step 3 Find 2,2. Subtract 0.05 from 1.000 to get 0,9500. The corresponding z value obtained from Table E is 1.65. (Note: This value is found by using the value for an area between 0.9495 and 0.9505. A more precise z value obtained mathematically is 1.645 and is sometimes used; however, 1.65 will be used in this text.) Step 4 Substitute in the formula X - 12 (#)