researcher obtains a sample of n 25 individuals from a popu

researcher obtains a sample of n = 25 individuals from a population with unknown parameters. If the sample mean is = 84 and standard deviation s = 100, then what value(s) of t should be used to construct a 90% confidence interval to estimate the population mean?

Solution

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)=84
Standard deviation( sd )=100
Sample Size(n)=25
Confidence Interval = [ 84 ± t a/2 ( 100/ Sqrt ( 25) ) ]
= [ 84 - 1.711 * (20) , 84 + 1.711 * (20) ]
= [ 49.78,118.22 ]

t-value = 1.711