Answered: calculate a 99% confidence interval for…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 13PPS

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Question

A computer information systems manager is debating which of two similarly priced laptop battery packs to purchase. He is interested in determining whether there is a difference in the average time the battery packs function before needing to be recharged.

Based on two independent random samples, the following summary information was computed:

Model 1

Sample size 15

Sample mean 6.2 hours

Sample standard deviation 2.6 hours

Model 2

Sample size 16 S

Sample mean 6.5 hours

Sample standard deviation 2.6 hours

Assuming normal populations with equal variances, calculate a 99% confidence interval for the difference in the average functioning time of the two models.

10 engineering schools were surveyed. The first random sample of 250 electrical engineers had 80 women, and the second random sample of 175 chemical engineers had 40 women. Obtain an 80% confidence interval for the difference in proportions of women in these two engineering fields.

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 + ...

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