Answer to Question #298651 in Statistics and Probability for praaveen

Question

Refer to Example 8. How large a sample will we need

in order to assert with probability 0.95 that the sample

mean will not differ from the true mean by more than

1.5. (replacing σ by s is reasonable here because the

estimate is based on a sample of size eighteen.)

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Below is the example 8

95% confidence interval for the mean of a normal population We know that silk fibers are very tough but in short supply. Engineers are making breakthroughs to create synthetic silk fibers that can improve everything from car bumpers to bullet-proof vests or to make artificial blood vessels . One research group reports the summary statistics1 n = 18 x = 22.6 s = 15.7 for the toughness (MJ/m3) of processed fibers. Construct a 95% confidence interval for the mean toughness of these fibers. Assume that the population is normal.

Reference book :- PROBABILITY AND STATISTICS FOR ENGINEERS (MILLER & FREUND’S) 9th edition. Page number :- 231