Answered: The diameter of a spindle in a small…

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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Question

For each situation, state the null and alternative hypotheses: (Type "mu" for the symbol ?μ , e.g. mu >> 1 for the mean is greater than 1, mu << 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1. Please do not include units such as "mm" or "$" in your answer.)

(a) The diameter of a spindle in a small motor is supposed to be 4.6 millimeters (mm) with a standard deviation of 0.11 mm. If the spindle is either too small or too large, the motor will not work properly. The manufacturer measures the diameter in a sample of 10 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 4.73 mm.
?0H0 :
??Ha :

(b) Harry thinks that prices in Caldwell are higher than the rest of the country. He reads that the nationwide average price of a certain brand of laundry detergent is $16.85 with standard deviation $1.15. He takes a sample from 3 local Caldwell stores and finds the average price for this same brand of detergent is $15.67.
?0H0 :
??Ha :

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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