Question

1. Suppose you would like to estimate the mean amount of money (μ) spent on books by CSIS students in a semester. You have the following data from 20 randomly selected CSIS students: X = $264 and s = $40. Assume that the amount spent on books by CSIS students is normally distributed.

a) Compute a 80% confidence interval.

b) Is there evidence at a 10% level of significance that the mean amount of money spent on books by CSIS students in a semester is not equal to $289?

Answer 1

X represents mean amount spent on books

So, 100(1-alpha)% confidence interval for mean amount spent is given by :

where , n = sample size . = 20

Here alpha = 0.2 , df = n-1 =19

So,

So, CI is :

b) At 10% level of significance ,

alpha = 0.10 ,

So, the confidence interval becomes:

Note that $ 289 does not fall in the above interval .

So we can say that , mean amount spent is not $289