you wish to test the following claim (Ha) at a significance level of α=0.02. Ho: μ= 81.6 Ha: μ> 81.6You believe the population is normally distributed and you know the standard deviation is σ=6.4. You obtain a sample mean of M=82.2 for a sample of size n=46.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is...less than (or equal to) αgreater than αThis test statistic leads to a decision to...reject the nullaccept the nullfail to reject the nullAs such, the final conclusion is that...There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 81.6.There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 81.6.The sample data support the claim that the population mean is greater than 81.6.There is not sufficient sample evidence to support the claim that the population mean is greater than 81.6.

Name: you wish to test the following claim (Ha) at a significance level of α
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Description: you wish to test the following claim (Ha) at a significance level of α=0.02. Ho: μ= 81.6 Ha: μ> 81.6You believe the population is normally distributed and you know the standard deviation is σ=6.4. You obtain a sample mean of M=82.2 for a sa

The test statistic is, z=M-μσn=82.2-81.66.446=0.60.9436=0.636 Thus, the test statistic is 0.636. The hypothesis is right tail. The p-value for right tailed test is, p-value=Pz>0.636=1-Pz<0.636 The probability of z less than 0.636 can be obtained using the excel formula “=NORM.S.DIST(0.636,TRUE)”. The probability value is 0.7376. The required p-value is, p-value=1-Pz<0.636=1-0.7376=0.2624 Thus, the p-value is 0.2624.Decision rule: If p-value≤α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis. Conclusion: The p-value (0.2624) is greater than the level of significance (0.02). Based on the decision rule, fail to reject the null hypothesis. Thus, there is not sufficient sample evidence to support the claim that the population mean is greater than 81.6.

Answered: you wish to test the following claim…

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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you wish to test the following claim (Ha) at a significance level of α=0.02.

H_o_: μ= 81.6
H_a_: μ> 81.6

You believe the population is normally distributed and you know the standard deviation is σ=6.4. You obtain a sample mean of M=82.2 for a sample of size n=46.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)

test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)

p-value =

The p-value is...

less than (or equal to) α
greater than α

This test statistic leads to a decision to...

reject the null
accept the null
fail to reject the null

As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 81.6.
There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 81.6.
The sample data support the claim that the population mean is greater than 81.6.
There is not sufficient sample evidence to support the claim that the population mean is greater than 81.6.

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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you wish to test the following claim (Ha) at a significance level of α=0.02. Ho: μ= 81.6 Ha: μ> 81.6 You believe the population is normally distributed and you know the standard deviation is σ=6.4. You obtain a sample mean of M=82.2 for a sample of size n=46.