Question

Assuming the random variable X is normally distributed, compute the upper and lower limit of the 90% confidence interval for the population mean if a random sample of size n=13 produces a sample mean of 40 and sample standard deviation of 4.38.

Lower Limit =  , Upper Limit =  
Round to two decimals.

Answer 1

Solution :

Given that,

t /2,df = 1.782

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

= 1.782 * (4.38 / 13)

Margin of error = E = 2.16

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

- E < < + E

40 - 2.16 < < 40 + 2.16

37.84 < < 42.16

lower limit: 37.84

upper limit: 42.16