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Name: The accuracy of a coin-counter machine is gauged to accept nickels wit
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Description: The accuracy of a coin-counter machine is gauged to accept nickels with a mean diameter of millimeters 21.21 mm. A sample of 39 nickles was drawn from a reported defective coin-counter machine located near a school. The sample had a sample mean of 21

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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The accuracy of a coin-counter machine is gauged to accept nickels with a mean diameter of millimeters 21.21 mm. A sample of 39 nickles was drawn from a reported defective coin-counter machine located near a school. The sample had a sample mean of 21.21 mm and sample standard deviation 0.011 mm.

Test the claim that the mean nickel diameter accepted by this coin-counter machine is greater than 21.21 mm. Test at the 0.1 significance level.

(a) Identify the correct alternative hypothesis HaHa:

μ>21.21μ>21.21
μ=21.21μ=21.21
μ<21.21μ<21.21

Give all answers correct to 4 decimal places.

(b) The test statistic value is:

(c) Using the Traditional method, the critical value is:

(d) Based on your asnwers above, do you:

(i) Reject H0H0

(ii) Fail to reject H0H0.

Explain your choice in the box below.

e) Based on your work above, choose one of the following conclusions of your test:

(i) the sample data supports the claim,

(ii) there is not sufficient evidence to support the claim,

(iii) there is sufficient evidence to warrant rejection of the claim

(iv) there is not sufficient evidence to warrant rejection of the claim.

Explain your choice in the box below.

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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