Question

QUESTION 11 "A local university administers a comprehensive examination to the recipients of a B.S. degree in Business Administration. A sample of 5 examinations is selected at random and scored. The scores are shown below. Assume the population is normally distributed 54 68 75 80 98 At 95% confidence, determine an interval for the mean of the population." 35.97 to 44.19 20.06 to 27.80 54.94 to 95.06 120.04 to 150.01

Answer 1

A sample of n=5 examination is selected at random and Scored. The scores are given as- 54, 68, 75, 80198 The sample mean is, 68+ 75+ 80+ 98) ła 5 (54768 757 the sample standard deviationis, sz 2 S-{(54-75)*7(68-7594175-75) +(80-75)²+(98-75) 16.155 We have to find a 95%. Confidence interval for population mean (pe). since sample size n25 <3o, we should use. t test statistic here. The formula for CI is

QI asy..? z łt t* s at - of .. * where, it is the tcritical value 20.025 and and degrees freedom, (n-1) 24 So, t* ² to 025,4 29:776 So, the feequired el, 75 + 2,776 16.155 ro 75 - 20.056, 75+ 20.05% 54.94, 95.06 so, thee Corvucl- option is, (e) .2