A random sample is drawn from a population of unknown standa

A random sample is drawn from a population of unknown standard deviation. Construct a 98% condence interval for the population mean based on the information given.

a. n= 225, x = 92.0,s= 8.4

b. n= 64, x = 92.0,s= 8.4

Solution

a)
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=92
Standard deviation( sd )=8.4
Sample Size(n)=225
Confidence Interval = [ 92 ± t a/2 ( 8.4/ Sqrt ( 225) ) ]
= [ 92 - 2.343 * (0.56) , 92 + 2.343 * (0.56) ]
= [ 90.688,93.312 ]
b)

Sample Size(n)=64
Confidence Interval = [ 92 ± t a/2 ( 8.4/ Sqrt ( 64) ) ]
= [ 92 - 2.387 * (1.05) , 92 + 2.387 * (1.05) ]
= [ 89.494,94.506 ]