BUSI 230 HW 8.2 Confidence Intervals for a Population Mean, Standard Deviation Unknown Assignment solutions complete answers
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When constructing a confidence interval for a population mean from a sample of size 20, the number of degrees of freedom for the critical value is .
Find the critical value needed to construct a confidence interval of the given level with the given sample size. Round the answer to at least three decimal places.
Online courses: A sample of 269 students who were taking online courses were asked to describe their overall impression of online learning on a scale of 1-7, with 7 representing the most favorable impression. The average score was 5.77, and the standard deviation was 0.98.
(a) Construct a 90% interval for the mean score. Round the answers to two decimal places.
(b) Assume that the mean score for students taking traditional courses is . A college that offers online courses claims that the mean scores for online courses and traditional courses are the same. Does the confidence interval contradict this claim? Explain.
Get an education: In 2012 the General Social Survey asked 844 adults how many years of education they had. The sample mean was 8.54 years with a standard deviation of 8.58 years.
(a) Construct a 99% interval for the mean number of years of education. Round the answers to two decimal places.
(b) Data collected in an earlier study suggest that the mean in was years. A sociologist believes that the mean in is the same. Does the confidence interval contradict this claim?
Sound it out: Phonics is an instructional method in which children are taught to connect sounds with letters or groups of letters. A sample of 136 first graders who were learning English were asked to identify as many letter sounds as possible in a period of one minute. The average number of letter sounds identified was 34.01 with a standard deviation of 23.83.
(a) Construct a 90% interval for the mean number of letter sounds identified in one minute. Round the answers to two decimal places.
(b) If a confidence interval were constructed with these data, would it be wider or narrower than the interval constructed in part (a)? Explain.
Baby weights: Following are weights, in pounds, of two–month–old baby girls. It is reasonable to assume that the population is approximately normal.
(a) Construct a 90% interval for the mean weight of two-month-old baby girls.
(b) According to the National Health Statistics Reports, the mean weight of two–month–old baby boys is pounds. Based on the confidence interval, is it reasonable to believe that the mean weight of two–month–old baby girls may be the same as that of two–month–old baby boys? Explain.
Sleeping outlier: A simple random sample of eight college freshmen were asked how many hours of sleep they typically got per night. The results were
Notice that one joker said that he sleeps 24 hours a day.
(a) The data contain an outlier that is clearly a mistake. Eliminate the outlier, then construct a 90% confidence interval for the mean amount of sleep from the remaining values. Round the answers to two decimal places.
(b) Leave the outlier in and construct the confidence interval. Round the answers to two decimal places.
