Question

In a study about how much College students sleep at night, a sample of 25 students was selected. The sample average mean number of hours of sleep was 6.64 and the sample standard deviation was 1.075.

(a) Construct a 90% confidence interval for the true mean number of hours of sleep at night College students get.

(b) Interpret the interval.

(c) What assumptions must be satisfied for the interval obtained in part (a) to be statistically valid?

Answer 1

Solution-A"

xbar=6.64

s=1.075

n=25

alpha=0.10

alpha/2=0.10/2=0.05

df=n-1=25-1=24

t critical in excel is

=T.INV(0.05,24)

=1.71088208

90% confidence interval for mean is

xbar-t*s/sqrt(n),xbar+t*s/sqrt(n)

6.64-1.71088208*1.075/sqrt(25),6.64+1.71088208*1.075/sqrt(25)

6.27216,7.00784

Solution-b:

we are90% confident that the true mean  umber of hours of sleep at night College students get lies in the interval

6.27216 and 7.00784

Solution-c:

assumptions are:

simple random sample

indpependent

sample follows normal distribution