A publisher wants to estimate the mean length of time (in minutes) all adults spend reading newspapers.  To determine this estimate, the publisher takes a random sample of 15 people and obtain the results below.  From past studies, the publisher assu;mes standard deviation is 1.9 minutes and that the population of times is normally distributed. 10   6  7   7  12    9   12   11  11   11   11  8   9    9   8 Construct the 90% and 99% confidence intervals for the population mean.  Which interval is wider? If convenient, use technology to construct the confidence intervals. The 90% confidence interval is _________ , ____________. (Round to one decimal place as needed) The 99% confidence interval is __________, ____________ (round to one decimal place as needed) Which interval is wider? The 99% confidence interval or The 90% confidence interval

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...