Preliminary data analysis indicate that it is reasonable to use a t-test to carry out the specified hypothesis test. Perform the t-test using the critical-value approach.Use a significance level of =α0.05 to test the claim that ≠μ30.5. The sample data consists of 10 scores for which =x36.2 and =s7.9. H0 : =μ36.2H1 : ≠μ36.2Test statistic: =t2.28. Critical values: =t±2.262. Reject H0 : =μ36.2.There is sufficient evidence to support the claim that the mean is different from 36.2. H0 : =μ30.5H1 : ≠μ30.5Test statistic: =t2.28. Critical values: =t±2.262. Reject H0 : =μ30.5.There is sufficient evidence to support the claim that the mean is different from 30.5. H0 : ≠μ36.2H1 : =μ36.2Test statistic: =t2.28. Critical values: =t±2.262. Reject H0 : =μ36.2.There is sufficient evidence to support the claim that the mean is different from 36.2. H0 : ≠μ30.5H1 : =μ30.5Test statistic: =t2.28. Critical values: =t±2.262. Reject H0 : =μ30.5.There is sufficient evidence to support the claim that the mean is different from 30.5.

Consider that μ is the population mean.

Answered: Preliminary data analysis indicate that…

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

Preliminary data analysis indicate that it is reasonable to use a

-test to carry out the specified hypothesis test. Perform the

-test using the critical-value approach.

Use a significance level of

=α0.05

to test the claim that

≠μ30.5

. The sample data consists of

scores for which

=x36.2

and

=s7.9

=μ36.2

≠μ36.2

Test statistic:

=t2.28

. Critical values:

=t±2.262

. Reject

=μ36.2

.
There is sufficient evidence to support the claim that the mean is different from

36.2

=μ30.5

≠μ30.5

Test statistic:

=t2.28

. Critical values:

=t±2.262

. Reject

=μ30.5

.
There is sufficient evidence to support the claim that the mean is different from

30.5

≠μ36.2

=μ36.2

Test statistic:

=t2.28

. Critical values:

=t±2.262

. Reject

=μ36.2

.
There is sufficient evidence to support the claim that the mean is different from

36.2

≠μ30.5

=μ30.5

Test statistic:

=t2.28

. Critical values:

=t±2.262

. Reject

=μ30.5

.
There is sufficient evidence to support the claim that the mean is different from

30.5

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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