Question

Wendy wants to estimate the mean number of hours that college students sleep each night. She obtains a simple random sample of 41 college students and finds that the sample mean is 6.7 with a standard deviation of 1.9. Construct a 90% confidence interval to estimate the population mean and interpret your answer in a complete sentence (round numbers to 1 decimal place).

Answer 1

Solution =

Given that,

n = 41

= 6.7   

s = 1.9

Note that, Population standard deviation() is unknown..So we use t distribution.

Our aim is to construct 90% confidence interval.   

c = 0.90

= 1- c = 1- 0.90 = 0.10

  /2 = 0.10 2 = 0.05

Also, d.f = n - 1 = 40  

    =    =  0.05,40 = 1.684

( use t table or t calculator to find this value..)

The margin of error is given by

E =  /2,d.f. * ( / n)

= 1.684 * ( 1.9 / 41 )

= 0.5

Now , confidence interval for mean() is given by:

( - E ) <   <  ( + E)

( 6.7 - 0.5 )   <   <  ( 6.7 + 0.5 )

6.2 <   < 7.2

Required 90% confidence interval is ( 6.2 , 7.2 )

Interpret :

The provided sample mean is \bar X = 6.7 and the sample standard deviation is s = 1.9 The size of the sample is n = 41 and the required confidence level is 90%.

Population standard deviation() is unknown..So we use t distribution.

Our aim is to construct 90% confidence interval.

Therefore, based on the information provided, the 90 % confidence for the population mean μ is ( 6.2 , 7.2 )