Answered: If, in a sample of n=25 selected from…

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

If, in a sample of n=25 selected from a normal population, X=59 and S=10,what is your statistical decision if the level of significance,α is 0.10, the null hypothesis, H0, is μ=50, and the alternative hypothesis, H1, is μ≠50?

a. Determine the critical value(s).

The critical value(s) is(are) ____________.

(Round to four decimal places as needed. Use a comma to separate answers as needed.)

b. Determine the test statistic, tSTAT. tSTAT=______________

(Round to four decimal places as needed.)

c. State your statistical decision. Choose the correct answer below.

A. The test rejects the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from μ=50.

B. The test does not reject the null hypothesis. The data provide

sufficient evidence to conclude that the mean differs from μ=50.

C. The test does not reject the null hypothesis. The data

does not provide sufficient evidence to conclude that the mean differs fromμ=50.

D. The test rejects the null hypothesis. The data does not provide sufficient evidence to conclude that the mean differs from μ=50.

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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