Reuben is a human resources executive for a technology company. He is deciding between two types of plans for vacation allowance for the employees of the company: Unlimited and Traditional. Reuben wants to determine, for workers in the tech industry, if the yearly mean number of vacation days taken by workers with an Unlimited plan is greater than the yearly mean number of vacation days taken by workers with a Traditional plan.Reuben surveys a random sample of 17 workers who have the Unlimited plan and a random sample of 15 workers who have the Traditional plan. (These samples are chosen independently.) For each worker, he records the number of vacation days taken last year. For the workers with an Unlimited plan, the sample mean is 18.9 with a sample variance of 30.8. For the workers with a Traditional plan, the sample mean is 17.4 with a sample variance of 6.1.Assume that the two populations of vacation days taken are approximately normally distributed. Can Reuben conclude, at the 0.10 level of significance, that the population mean of the yearly number of vacation days taken by workers with an Unlimited plan is greater than the population mean of the yearly number of vacation days taken by workers with a Traditional plan? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) A. Find the value of the test statistic. (Round to three or more decimal places.) B. Find the p-value. (Round to three or more decimal places.) C. At the 0.10 level of significance, can Reuben conclude that the yearly mean number of vacation days taken by workers with an Unlimited plan is greater than the yearly mean number of vacation days taken by workers with a Traditional plan?

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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Reuben is a human resources executive for a technology company. He is deciding between two types of plans for vacation allowance for the employees of the company: Unlimited and Traditional. Reuben wants to determine, for workers in the tech industry, if the yearly mean number of vacation days taken by workers with an Unlimited plan is greater than the yearly mean number of vacation days taken by workers with a Traditional plan.Reuben surveys a random sample of 17 workers who have the Unlimited plan and a random sample of 15 workers who have the Traditional plan. (These samples are chosen independently.) For each worker, he records the number of vacation days taken last year. For the workers with an Unlimited plan, the sample mean is 18.9 with a sample variance of 30.8. For the workers with a Traditional plan, the sample mean is 17.4 with a sample variance of 6.1.Assume that the two populations of vacation days taken are approximately normally distributed. Can Reuben conclude, at the 0.10 level of significance, that the population mean of the yearly number of vacation days taken by workers with an Unlimited plan is greater than the population mean of the yearly number of vacation days taken by workers with a Traditional plan? Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)

A. Find the value of the test statistic. (Round to three or more decimal places.)

B. Find the p-value. (Round to three or more decimal places.)

C. At the 0.10 level of significance, can Reuben conclude that the yearly mean number of vacation days taken by workers with an Unlimited plan is greater than the yearly mean number of vacation days taken by workers with a Traditional plan?

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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