Download 9.1.2 Confidence Interval - Known SD

Confidence Intervals about a Population Mean
Page 1
Old Faithful Confidence Interval
1. The following data set represents a simple random sample of the interval of time (in minutes)
between eruptions of Old Faithful in Yellowstone Park. Assume that the standard deviation
of all intervals between eruptions is known to be 10.5 from previous observations. Find the
90% confidence interval for the mean interval of time between eruptions.
70
61
75
77
73
57
69
81
81
91
73
77
80
90
51
61
62
75
79
67
2. Suppose park rangers want to conduct an observational study of Old Faithful in Yellowstone
Park to help visitors plan their trip to the park. Determine the sample size needed to be 99%
confident that the true mean interval of time between eruptions is within 30 seconds.
(Remember the standard deviation is known to be 10.5 minutes).
Robert A. Powers
University of Northern Colorado
Confidence Intervals about a Population Mean
Page 2
Lake Wobegon IQ Test Scores
Residents of Lake Wobegon1 claim that their town is a place, “where the women are strong, the
men are good looking, and all of the children are above average.” A researcher decides to collect
the IQ test scores of 31 elementary school students. Below are the data obtained.
114 100 104 89 102 91 114 114 103 105 108 130 120 132 111 128
118 119 86 72 111 103 74 112 107 103 98 96 112 112 93
The standard deviation of the IQ scores of elementary students in the U.S. is σ = 16. Find the
90% confidence interval for the mean IQ test scores of elementary students of Lake Wobegon.
2. Suppose educators want to conduct an observational study of elementary students in all of
Mist County, Minnesota2. Determine the sample size needed to be 99% confident that the
true IQ test score is within 10 points.
1
Lake Wobegon is a fictitious town in Minnesota create by Garrison Keillor in his radio program A Prairie Home
Companion
2
Also fictitious.
Robert A. Powers
University of Northern Colorado