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Name: Estimate population mean (σ is known): A manufacturer of women’s cloth
Uploaded: 2024-03-20T07:07:12.000Z
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Description: Estimate population mean (σ is known): A manufacturer of women’s clothing wants to know the mean height of the women in a town (in order to plan what proportion of garments should be of each size). She knows that the standard deviation of their heigh

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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Estimate population mean (σ is known): A manufacturer of women’s clothing wants to know the mean height of the women in a town (in order to plan what proportion of garments should be of each size). She knows that the standard deviation of their heights is 5 cm. She selects a random sample of 50 women from the town and finds their mean height to be 165.2 cm

(a) Construct a 90% confidence interval for the mean height of women in the town. (Round to two decimal places)

(b) Another manufacturer in the same town wants to know the mean height of women in the town to within 0.5 cm with 98% confidence. What is the minimum sample size that would ensure this? (Round to the nearest whole number):

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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