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Description: Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original

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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Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

A coin mint has a specification that a particular coin has a mean weight of

2.52.5

g. A sample of

3333

coins was collected. Those coins have a mean weight of

2.493792.49379

g and a standard deviation of

0.011290.01129

g. Use a

0.050.05

significance level to test the claim that this sample is from a population with a mean weight equal to

2.52.5

g. Do the coins appear to conform to the specifications of the coin mint?

What are the hypotheses?

Upper H 0H0:

muμequals=2.52.5

Upper H 1H1:

muμless than<2.52.5

Upper H 0H0:

muμnot equals≠2.52.5

Upper H 1H1:

muμequals=2.52.5

Upper H 0H0:

muμequals=2.52.5

Upper H 1H1:

muμgreater than or equals≥2.52.5

Upper H 0H0:

muμequals=2.52.5

Upper H 1H1:

muμnot equals≠2.52.5

Your answer is correct.

Identify the test statistic.

tequals=nothing

(Round to three decimal places as needed.)

What is the P-Value?

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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