A pet food producer manufactures and then fills 25-pound bags of dog food on two different production lines located in separate cities. In an effort to determine whether differences exist between the average fill rates for the two lines, a random sample of 19 bags from line 1 and a random sample of 23 bags from line 2 were recently selected. Each bag’s weight was measured and the following summary measures from the samples were reported: Production Line 1 Production Line 2 Sample Size, n 19 23 Sample Mean, x 24.96 25.01 Sample Standard Deviation, s 0.07 0.08 Management believes that the fill rates of the two lines are normally distributed with equal variances. a) Calculate the point estimate for the difference between the population means of the two lines. b) Develop a 95% confidence interval estimate of the true mean difference between the two lines. c)Based on the 95% confidence interval estimate calculated in part b, what can the managers of the production lines conclude about the differences between the average fill rates for the two lines

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Description: A pet food producer manufactures and then fills 25-pound bags of dog food on two different production lines located in separate cities. In an effort to determine whether differences exist between the average fill rates for the two lines, a random sam

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A pet food producer manufactures and then fills 25-pound bags of dog food on two different production lines located in separate cities. In an effort to determine whether differences exist between the average fill rates for the two lines, a random sample of 19 bags from line 1 and a random sample of 23 bags from line 2 were recently selected. Each bag’s weight was measured and the following summary measures from the samples were reported:

Production Line 1 Production Line 2

Sample Size, n 19 23

Sample Mean, x 24.96 25.01

Sample Standard Deviation, s 0.07 0.08

Management believes that the fill rates of the two lines are normally distributed with equal variances.

a) Calculate the point estimate for the difference between the population means of the two lines.

b) Develop a 95% confidence interval estimate of the true mean difference between the two lines.

c)Based on the 95% confidence interval estimate calculated in part b, what can the managers of the production lines conclude about the differences between the average fill rates for the two lines?

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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