Answered: years. A survey of companies reported…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 4GP

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A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least nine years. A survey of companies reported in The Wall Street Journal found a sample mean tenure of x = 7.27 years for CEOs with a standard deviation of s = 6.38 years.

(a)

Formulate hypotheses that can be used to challenge the validity of the claim made by the shareholders' group.

H₀: μ = 9

H_a: μ ≠ 9

H₀: μ < 9

H_a: μ ≥ 9

H₀: μ ≥ 9

H_a: μ < 9

H₀: μ ≤ 9

H_a: μ > 9

H₀: μ > 9

H_a: μ ≤ 9

(b)

Assume 90 companies were included in the sample.

What is the test statistic? (Round your answer to three decimal places.)

( )

What is the p-value for your hypothesis test? (Round your answer to four decimal places.)

p-value =

what is your conclusion?

Do not reject H₀. We cannot conclude that the mean tenure of a CEO is significantly lower than 9 years. The claim of the shareholders group is valid.

Do not reject H₀. We can conclude that the mean tenure of a CEO is significantly lower than 9 years. The claim of the shareholders group is not valid.

Reject H₀. We cannot conclude that the mean tenure of a CEO is significantly lower than 9 years. The claim of the shareholders group is valid.

Reject H₀. We can conclude that the mean tenure of a CEO is significantly lower than 9 years. The claim of the shareholders group is not valid.

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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