You wish to test the following claim (HaHa) at a significance level of α=0.02α=0.02. Ho:μ=76.3Ho:μ=76.3 Ha:μ<76.3Ha:μ<76.3You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=25n=25 with mean M=72.5M=72.5 and a standard deviation of SD=17.3SD=17.3.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) ααgreater than ααThis 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 less than 76.3.There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 76.3.The sample data support the claim that the population mean is less than 76.3.There is not sufficient sample evidence to support the claim that the population mean is less than 76.3.

From provided information, Claim is: Ho: μ=76.3Ha: μ<76.3 Data is: Population is normally distributed, population standard deviation is unknown. n=25 M=72.5 S.D.=17.3Test statistic for this sample is: t=M-μS.D/n=72.5-76.317.3/25=-1.0983 Thus, test statistic is -1.098.The test is one tailed. The p value of the test statistic from the standard normal table is 0.1415. The level of significance (α) = 0.02 Decision rule: Reject H0: if p value < level of significance (α) Since, the p value is 0.1415 which is greater than level of significance, therefore, the null hypothesis would be failed to reject. Conclusion is: There is not sufficient sample evidence to support the claim that the population mean is less than 76.3.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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

Ho:μ=76.3Ho:μ=76.3
Ha:μ<76.3Ha:μ<76.3

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=25n=25 with mean M=72.5M=72.5 and a standard deviation of SD=17.3SD=17.3.

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) αα
greater than αα

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 less than 76.3.
There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 76.3.
The sample data support the claim that the population mean is less than 76.3.
There is not sufficient sample evidence to support the claim that the population mean is less than 76.3.

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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