Question

A researcher is interested in finding a 95% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 96 students who averaged 37.1 minutes concentrating on their professor during the hour lecture. The standard deviation was 13.6 minutes. Round answers to 3 decimal places where possible. a. To compute the confidence interval use a distribution. b. With 95% confidence the population mean minutes of concentration is between and minutes. c. If many groups of 96 randomly selected members 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 minutes of concentration.

Answer 1

(a) The Confidence interual use t- distribution because population Standard deviation is unknown. 16) 2-1-0.95 = 0.05 =hl -96-1 -95 B = 37.1, 5=1316, n=96,6=950), &=1-0,95 = 0.05 | df = n! & lg = 0.025 taya, df = +0.025,95 = +(1.985) (using t table] 95% Confidence interval for the mean = X † tafa, et see on = 37.1 I 1.985 x 13.6 (C) i man - 37.1 [ .75597 = 34.3447, 39.8553 95"). CI = 34.345 39.855 if many groups of 96 randomly selected members are studied, then a different confidence interval would be produced from each group, about 95% of these confidence interval will contain the true population mean min. of concentration and about 5 percent will not contain the true Population mean minutes of concentration.