Question

Suppose a random sample of 25 is drawn from a population whose standard deviation is unknown. If the sample mean is 125 and the sample standard deviation is 10, the 90% confidence interval to estimate the population mean is between

Answer 1

Given that,

= 125

s =10

n = 25

Degrees of freedom = df = n - 1 = 25- 1 = 24

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,24 = 1.711    ( using student t table)

Margin of error = E = t/2,df * (s /n)

=1.711 * ( 10/ 25) = 3.4220

The 90% confidence interval estimate of the population mean is,

- E < < + E

125 - 3.4220 < < 125+ 3.4220

121.5780 < < 128.4220

( 121.5780 ,128.4220)