Answered: A simple random sample of size n=40 is…

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

100%

A simple random sample of size

n=40

is drawn from a population. The sample mean is found to be

107.6,

and the sample standard deviation is found to be

20.2.

Is the population mean greater than

100

at the

α=0.025

level of significance?

Determine the null and alternative hypotheses.

H0:

mu equals 100μ=100

mu less than 100μ<100

mu equals 100μ=100

mu greater than 100μ>100

mu less than 107.6μ<107.6

mu equals 107.6μ=107.6

mu greater than 107.6μ>107.6

H1:

mu greater than 100μ>100

mu less than 100μ<100

mu equals 100μ=100

mu greater than 100μ>100

mu less than 107.6μ<107.6

mu equals 107.6μ=107.6

mu greater than 107.6μ>107.6

Compute the test statistic.

t 0t0

z 0z0

(Round to two decimal places as needed.)

Determine the P-value.

The P-value is

(Round to three decimal places as needed.)

What is the result of the hypothesis test?

the null hypothesis because the P-value is

the level of significance. At the

α=0.025

level of significance, the population mean

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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