A shareholders' group is lodging a protest against your company. The shareholders group claimed that the mean tenure for a chief exective office (CEO) was at least 8 years. A survey of 117 companies reported in The Wall Street Journal found a sample mean tenure of 6.5 years for CEOs with a standard deviation of s=s= 4.6 years (The Wall Street Journal, January 2, 2007). You don't know the population standard deviation but can assume it is normally distributed. You want to formulate and test a hypothesis that can be used to challenge the validity of the claim made by the group, at a significance level of α=0.05α=0.05. Your hypotheses are: Ho:μ≥8Ho:μ≥8 Ha:μ<8Ha:μ<8 What is the test statistic for this sample? test statistic = (Report answer accurate to 3 decimal places.) What is the p-value for this sample? p-value = (Report answer accurate to 4 decimal places.) The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is less than 8. There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 8. The sample data support the claim that the population mean is less than 8. There is not sufficient sample evidence to support the claim that the population mean is less than 8.

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 shareholders' group is lodging a protest against your company. The shareholders group claimed that the mean tenure for a chief exective office (CEO) was at least 8 years. A survey of 117 companies reported in The Wall Street Journal found a sample mean tenure of 6.5 years for CEOs with a standard deviation of s=s= 4.6 years (The Wall Street Journal, January 2, 2007). You don't know the population standard deviation but can assume it is normally distributed.

You want to formulate and test a hypothesis that can be used to challenge the validity of the claim made by the group, at a significance level of α=0.05α=0.05. Your hypotheses are:

      Ho:μ≥8Ho:μ≥8
      Ha:μ<8Ha:μ<8

What is the test statistic for this sample?
test statistic =  (Report answer accurate to 3 decimal places.)

What is the p-value for this sample?
p-value =  (Report answer accurate to 4 decimal places.)

The p-value is...

less than (or equal to) αα
greater than αα

This test statistic leads to a decision to...

reject the null
accept the null
fail to reject the null

As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the population mean is less than 8.
There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 8.
The sample data support the claim that the population mean is less than 8.
There is not sufficient sample evidence to support the claim that the population mean is less than 8.

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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