Question

A college admissions officer for an MBA program has determined that historically applicants have undergraduate grade point averages that are normally dis- tributed with a standard deviation of 0.4. From a random sample of 16 applications from the current year, the sample mean grade point average is 2.5. (a) (5 points) Find a 95% confidence interval for the population mean. (b) Based on these sample results, a statistician computes for the popula- tion mean a confidence interval extending from 2.39 to 2.61. Find the confidence level (1 - a) associated with this interval.

Answer 1

for part (b) level of significance =30% therefore confidence interval is 70%

# Sa = 6 = 0.4 h=16, X = 2.5 (a) 95000 conyidence interval XI tal- SLE = 2.5+ 2010. 004 16 2.5 + 2.120.0.4 4 2.5+ 0.212 = 2.288 le a 2.712 (b) Poluation mean confidence interval 2.39 to 2061 2.39 = X-tal.se Tn 205-talo 0.4 4 tal- O. 0.4 4 2.5-2.39 = tala 0011 O For n=16 ta/= to 15 =) d= 30 30% we have Con Tidence interval = 70%