You wish to test the following claim at a significance level of a=0.10. H0:U=81.8 H1:U<81.8You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size 90 with mean 77.6 and a standard deviation of 14.8.What is the test statistic for this sample? (Report answer accurate to 3 decimal places.)What is the p-value for this sample? (Report answer accurate to 4 decimal places.)This test statistic leads to a decision toreject the nullaccept the nullfail to reject the nullAs such, the final conclusion is thatthere is sufficient evidence to conclude that the population mean is equal to 81.8.there is not sufficient evidence to conclude that the population mean is equal to 81.8.there is sufficient evidence to conclude that the population mean is less than 81.8.there is not sufficient evidence to conclude that the population mean is less than 81.8.

The hypothesis is H0: μ=81.8 vs Ha: μ<81.8 Sample size, n=90 Sample mean, x¯=77.6 Sample standard…

Answered: You wish to test the following claim at…

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

You wish to test the following claim at a significance level of a=0.10.

H0:U=81.8
H1:U<81.8

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size 90 with mean 77.6 and a standard deviation of 14.8.

What is the test statistic for this sample? (Report answer accurate to 3 decimal places.)

What is the p-value for this sample? (Report answer accurate to 4 decimal places.)

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 conclude that the population mean is equal to 81.8.
there is not sufficient evidence to conclude that the population mean is equal to 81.8.
there is sufficient evidence to conclude that the population mean is less than 81.8.
there is not sufficient evidence to conclude that the population mean is less than 81.8.

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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