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1400 - 3.250(6.325) divide the values 71 = (2.15)2 > square n = 462.25 > Round up the value to 463 So, the required sample size is 463 six-year old children. 3. Zeanne wants to replicate a study where the lowest observed value is 12.4 while the highest is 12.8. He wants to estimate the population mean to within an error of 0.025 of its true value. Using 97% confidence level, find the sample size n that he needs. Given: Confidence interval = 97% ; therefore, Za/2 = 2.17. The desired error is 0.025. Since the range R = 12.8 - 12.4 = 0.4, then R 04 = 0.1 4 Solutions: n= > substitute values in the formula (2.17 )(0.1)12 n = 0.025 > multiply 2.17 and 0.1 71 = (0.217 0.025 > divide values inside the quantity sign (). n = (8.68)2 > square 71 = 75.34 > Round up to 76. So, the required sample size is 76. EVALUATION: Solve the following problems. 1. A sample of 50 Asian women showed a mean height of 60 inches. If it is known that the standard deviation of heights of Asian women is 2.5 inches, construct a 95% confidence interval estimate for the height of all Asian women. 2. An engineer wants to determine the average time that it takes to drill a hole in a certain metal type. How large a sample will he need to be 98% confident that his sample mean within 8 seconds within the true population mean? Use the result of the previous study that the population standard deviation of this drill time is 25 seconds. 3. A media research company wants to construct a 95% confidence interval estimate of the mean amount of time senior high school students spend watching TV per day. To do this, they have randomly selected 60 senior high school students. After an interview, the samples showed that their mean amount of watching TV is 25 minutes with standard deviation of 3.5 minutes. Help the media to construct the interval estimate.2.052 2.771 28 27 1.703 2.048 2.763 28 1.701 29 2.045 2.756 30 29 1:699 2.750 1.697 2.042 31 30 2.021 2.714 40 1.684 41 2.000 2.660 61 60 1.671 2.576 1.645 1.960 Examples: 1. Compute the margin of error of the 90% confidence interval estimate of , when's - S and n- 16. Solution: ta/z () = 1.753 ( ) = 1.753 () = 1.753(1.25) = 2.19 2. Compute the 95% confidence interval estimate of u given the following: s =9,n = 12, and x = 27 Solution: * - ta/2()