Answered: cell phone company offers two plans to…

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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Question

A cell phone company offers two plans to its subscribers. At the time new subscribers sign up, they are asked to provide some demographic information. The mean yearly income for a sample of 34 subscribers to Plan A is $48,450 with a standard deviation of $7,820. For a sample of 26 subscribers to Plan B, the mean income is $51,850 with a standard deviation of $6,052.

At the 0.050 significance level, is it reasonable to conclude the mean income of those selecting Plan B is larger?

a. What are the null and alternate hypotheses?

multiple choice 1

H₀: μ_A≥ μ_BH₁: μ_A< μ_B
H₀: μ_A≥ μ_BH₁: μ_A> μ_B
H₀: μ_A≤ μ_BH₁: μ_A< μ_B

b. Compute the test statistic. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)

c. Compute the p-value. NOTE: P-value calculators are available through online search. (Round your answer to 4 decimal places.)

d. What is your decision regarding the null hypothesis?

multiple choice 2

Reject H₀ Correct
Fail to reject H₀

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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