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Name: Your firm manufactures medicine which is dispensed into bottles. The m
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Description: Your firm manufactures medicine which is dispensed into bottles. The mean fill level for the medicine bottles is supposed to be 200 ml. You take a random sample of 13 bottles and find the following fill levels (in milliliters): 195, 195, 200, 198, 2

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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Your firm manufactures medicine which is dispensed into bottles. The mean fill level for the medicine bottles is supposed to be 200 ml. You take a random sample of 13 bottles and find the following fill levels (in milliliters):

195, 195, 200, 198, 204, 195, 201, 199, 204, 195, 196, 202, 199

Assume that the fill levels are Normally distributed in the entire population. Assume that the population standard deviation for all fill levels of medicine bottles σ is unknown.

Construct and interpret 90% confidence interval for the mean fill level μ of medicine bottle. Write a statement which correctly states the meaning of this interval in the context of the problem.

Round all final answers to 2 decimal places, if needed.

(a) The average fill level for the sample of 13 medicine bottles is

(b) We are 90% confident that the mean fill level of medicine bottles μ is between and (milliliters)

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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