A national corporation has implemented incentives for employees to engage in a fitness program. The program has been in effect for 3 years and the corporation claims that the average BMI among its male employees is lower than the national average for males. The CDC list the average BMI for males to be 26.6. Sample size = 40, sample mean = 25.74, standard deviation = 6.16557Perform a hypothesis test at a level of significance of 0.05 to examine the claim by the corporation with respect to having a lower average BMI than the national average. Clearly state the hypotheses, Determine the rejection region, Compute the test statistic, Clearly state if the null hypothesis can be rejected and why or why not, Determine the p-value of the test and interpret all results of the hypothesis test. Also Determine 95% confidence interval about the population mean and 90% confidence interval about the population mean. For both parts 95% and 90%, make a statement about the ability to either support or reject the employer’s claim.

Hypothesis test are used to compare the sample and population significance. If the population…

Answered: A national corporation has implemented…

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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A national corporation has implemented incentives for employees to engage in a fitness program. The program has been in effect for 3 years and the corporation claims that the average BMI among its male employees is lower than the national average for males. The CDC list the average BMI for males to be 26.6. Sample size = 40, sample mean = 25.74, standard deviation = 6.16557

Perform a hypothesis test at a level of significance of 0.05 to examine the claim by the corporation with respect to having a lower average BMI than the national average. Clearly state the hypotheses, Determine the rejection region, Compute the test statistic, Clearly state if the null hypothesis can be rejected and why or why not, Determine the p-value of the test and interpret all results of the hypothesis test. Also Determine 95% confidence interval about the population mean and 90% confidence interval about the population mean. For both parts 95% and 90%, make a statement about the ability to either support or reject the employer’s 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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