Question

A sample of 25 items yields X = 60 grams and s = 5 grams. Assuming a normal parent distribution, construct a 99 percent confidence interval for the population mean weight.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 60

sample standard deviation = s = 5

sample size = n = 25

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

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df = 2.797

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

= 2.797* ( 5 / 25)

Margin of error = E = 2.797

The 99% confidence interval estimate of the population mean is,

- E < < + E

60 - 2.797 < < 60 + 2.797

57.203 < < 62.797

( 57.203 , 62.797 )