Answered: like to know the population mean, you…

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

Probability is: 0.9229

Hours 1.6448

Since the operations manager would like to know the population mean, you decide to help him conduct a hypothesis test for the population mean. Based on the random sample of 800 humidifiers that he selects, you find that the sample mean life of the humidifiers is 18017 hours. Continue to assume that based on past experience, the population standard deviation is 800 hours and the vacuum's service life is normally distributed. Answer the following questions related to conducting this hypothesis test:

h0= 18000

h1= 18000

d. State the appropriate test used and reason. Determine the appropriate test statistic. Keep at least 2 decimal places. (Hint: for calculating the test statistic, consider the sample mean value obtained from the random sample you have found above)

Appropriate test used and reason:

Test Statistic:

Critical Value: 1.96

f. Based on your answer in part e, is there evidence that the population mean life of humidifiers is different from 18000 hours (use α = 0.05)? Explain by providing the decision and conclusion.

g. Compute the p-value and interpret its meaning under the condition that the null hypothesis is true. Keep at least 4 decimal places.

p-value:

please use excel to solve

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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