Question

A manufacturer has a set of data for a random sample Yi as follows:

3005 2925 2935 2995 2937 2905

Assume that Yi is approximately normally distributed random sample. Find a 99% confidence interval for the population mean µ

Answer 1

n= 6, c= 99%

calculate mean and standard deviation for given sample data we get

sample standard deviation (s) = 40.233

sample mean () = 2950.33

formula for confidence interval is

where tc is the t critical value for c= 99% with df= n-1 =6-1 =5

we get

tc= 4.032

2950.33−66.228 <   < 2950.33+66.228

2884.102 <   < 3016.558

Confidence interval is = ( 2884.102 , 3016.558 )