Question

A survey was conducted that asked 1019 people how many books they had read in the past year. Results indicated that x overbarequals10.9 books and sequals16.6 books. Construct a 99​% confidence interval for the mean number of books people read. Interpret the interval.

Construct a

99​%

confidence interval for the mean number of books people read and interpret the result. Select the correct choice below and fill in the answer boxes to complete your choice.

​(Use ascending order. Round to two decimal places as​ needed.)

A.If repeated samples are​ taken,

9999​%

of them will have a sample mean between

nothing

and

nothing.

B.There is

9999​%

confidence that the population mean number of books read is between

blank

and

blank

C.There is a

9999​%

chance that the true mean number of books read is between

nothing

and

nothing.

Answer 1

Here, we have given that,

n= Number of people read many books past year= 1019

= sample mean = 10.9 books

s=sample standard deviation = 16.6 books

Now, we want to find the 99% confidence interval for population mean (number of books peopole read)

Formula is as follows,

Where

E=Margin of error =

Now, first we find the critical value

Degrees of freedom = n-1 = 1019-1=1018

c=confidence level =0.99

=level of significance=1-c=1-0.99=0.01

and we know that confidence interval is always two tailed

t-critical =2.581  ( using t table )

Now,

E=

=

=1.342

we get the margin of error E= 1.342

We get the 99% confidence interval for the population mean

Interpretation:

This is the 99% CI which shows that we have 90% confidence that this population mean will fall within this interval.