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 2020-11-09 Answered
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.
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Expert Answer

Obiajulu
Answered 2020-11-10 Author has 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.

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