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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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.

Obiajulu · Accepted Answer

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=n−1 =117−1 =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=x―−tα/2(sn)&amp;lt;μ&amp;lt;x―+tα/2(sn) =40.9−1.658(11.8117)&amp;lt;μ&amp;lt;40.9+1.658(11.8117) =40.9−1.658(1.090910386)&amp;lt;μ&amp;lt;40.9+1.658(1.090910386) =40.9−1.80872942&amp;lt;μ&amp;lt;40.9+1.80872942 =39.09127058&amp;lt;μ&amp;lt;42.70872942 =39.091&amp;lt;μ&amp;lt;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.

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

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