A study was conducted to estimate the mean amount spent on Christmas gifts for a

Question

A study was conducted to estimate the mean amount spent on Christmas gifts for a typical family having two children. A sample of size 150 was taken, and the mean amount spent was $225. Assuming a standard deviation equal to $50, find a 95% confidence interval for mu , the mean for all such families. 217 to 233 220 to 243 220 to 233 217 to 220 A sample was selected from a normal population with a standard deviation sigma = 6.1. The sample values are 114, 120, 108, 118, 119, 123, 117, 124, 115, and 129. Construct a confidence interval estimate of the population mean with 0.90 level of confidence. 113.72 to 123.68 114.92 to 122.48 115.52 to 121.88 114 to 125

Explanation / Answer

(1) Given n=150, xbar=225, s=50, =0.05, Z(0.025)=1.96 (checknormal table) The 95% CI is xbar ± Z*s/n --> 225 ± 1.96*50/sqrt(150) --> ( 216.9983, 233.0017) Answer: a (2) Given =6.1, n=10, xbar=118.7, s= 5.85 (based on thedata) =0.1, Z(0.05)=1.645 (check normal table) The 90% CI is xbar ± Z*s/n --> 118.7 ± 1.645*5.85/sqrt(10) --> (115.65, 121.74) Answer: C xbar

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