A researcher is interested in finding a 90% confidence interval for the mean number minutes students are concentrating on their professor during a one

Bergen

Bergen

Answered question

2020-11-09

A researcher is interested in finding a 90% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 117 students who averaged 40.9 minutes concentrating on their professor during the hour lecture. The standard deviation was 11.8 minutes. Round answers to 3 decimal places where possible.
a.
To compute the confidence interval use a ? distribution.
b.
With 90% confidence the population mean minutes of concentration is between ____ and ____ minutes.
c.
If many groups of 117 randomly selected students are studied, then a different confidence interval would be produced from each group. About ____ percent of these confidence intervals will contain the true population mean minutes of concentration and about ____ percent will not contain the true population mean number of minutes of concentration.

Answer & Explanation

Obiajulu

Obiajulu

Skilled2020-11-10Added 98 answers

Step 1
Given: x=40.9,s=11.8,n=117
a)
The sampling distribution follows a t-distribution.
Reason:
Since the population standard deviation is unknown, so the t-distribution is appropriate
b)The degree of freedom is,
df=n1
=1171
=116
Critical value:
By using the t-tables, the critical value at 10% level of significance for a two tailed t -distribution is,
t0.10/2.116=±1.658
Step 2
The 90% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture is,
90%CI=xtα/2(sn)<μ<x+tα/2(sn)
=40.91.658(11.8117)<μ<40.9+1.658(11.8117)
=40.91.658(1.090910386)<μ<40.9+1.658(1.090910386)
=40.91.80872942<μ<40.9+1.80872942
=39.09127058<μ<42.70872942
=39.091<μ<42.709
With 95% confidence the population the mean minutes of concentration is between 39.091 and 42.709.
c)
If many groups of 117 randomly selected students are studied, then a different confidence interval would be produced from each group. About 95 percent of these confidence intervals will contain the true population mean number of minutes of concentration and about 5 percent will not contain the true population mean number of minutes of concentration.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?