The health of employees is monitored by periodically weighing them in. A sample of 54 employees has a mean weight of 185.6 lb. with a standard deviation of 125.6 lb. Use a 0.10 significance level to test the claim that the mean weight of all such employees is less than 200 lb. a. Define the parameter A. mu = The mean weight of all such employees B. p = The proportion of all such employees who weigh less than 200 lb. C. mu = The mean weight lost by all such employees D. mu = The mean weight of the 54 employees b. State the null and alternative hypotheses A. Upper H 0 : mu equals 200 Upper H 1 : mu not equals 200 B. Upper H 0 : mu equals 185.6 Upper H 1 : mu less than 185.6 C. Upper H 0 : mu equals 200 Upper H 1 : mu greater than 200 D. Upper H 0 : mu equals 200 Upper H 1 : mu less than 200 c. Calculate the P-value. Which of these options is closest to its value? A. 0.2016 B. 0.1822 C. 0.1486 D. 0.2195 d. State the technical conclusion A. Reject Upper H 0 B. Do not reject Upper H 0 e. State the final conclusion A. There is not sufficient evidence to warrant rejection of the claim. B. There is sufficient evidence to warrant rejection of the claim. C. There is not sufficient sample evidence to support the claim. D. The sample data support the 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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The health of employees is monitored by periodically weighing them in. A sample of 54 employees has a mean weight of

185.6

lb. with a standard deviation of

125.6

lb. Use a 0.10 significance level to test the claim that the mean weight of all such employees is less than 200 lb.

a. Define the parameter

= The mean weight of all such employees

p = The proportion of all such employees who weigh less than 200 lb.

= The mean weight lost by all such employees

= The mean weight of the 54 employees

b. State the null and alternative hypotheses

Upper H 0 : mu equals 200 Upper H 1 : mu not equals 200

Upper H 0 : mu equals

185.6

Upper H 1 : mu less than

185.6

Upper H 0 : mu equals 200 Upper H 1 : mu greater than 200

Upper H 0 : mu equals 200 Upper H 1 : mu less than 200

c. Calculate the P-value. Which of these options is closest to its value?

0.2016

0.1822

0.1486

0.2195

d. State the technical conclusion

Reject Upper H 0

Do not reject Upper H 0

e. State the final conclusion

There is not sufficient evidence to warrant rejection of the claim.

There is sufficient evidence to warrant rejection of the claim.

There is not sufficient sample evidence to support the claim.

The sample data support the claim.

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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