Question

A clinic offers a weight loss program. The table below gives the amounts of weight loss, in pounds, for a random sample of 20 of its clients at the conclusion of the program. Assume that the data are normally distributed. Complete parts (a) and (b). 9 B 10 B 23 17 13 19 16 24 15 11 17 7 10 22 24 18 15 The 99% confidence interval is from a lower limit of to an upper limit of (Round to two decimal places as needed) b. Without doing the calculations, explain whether a 90% confidence interval for the population mean would be wider than, narrower than, or the same as that found in part (a). Choose the correct answer below O A. It will be narrower because the margin of error wil be larger for a 90% confidence interval than for a 90% confidence interval OB. It will be wider because the margin of error will be larger for a 90% confidence interval than for a 99% confidence interval. OC. It will be the same because the confidence interval is being calculated for the same data set OD. It will be narrower because the margin of error will be smaller for a 90% confidence interval than for a 99% confidence interval

Answer 1

The 99% C.I. for population mean is +] s tnt,& where = AVERAGE (23, 17, --- 30) = 15.8 Using MS-Excel S= STDEV.S (23, 17, 30) = 6.445 tnt, d/ t 20-1, o.o n = 20 1-030.99 = 730001 tig, orol TINV CO. 01, 19) 2.861 .: C.I. C { Using MS- Excel 3.1) 15.8 6.445 + * 2.86 | 20 15.8 7 4012 ) (11.68, 19.92) The gg % confidence ice interval is from a lower limit of 11.68 an upper limit 19.92 6 D. It will be narrower because the margin of error will be smaller for 90% confidence interval than for a 99% confidence interval. a