Answered: . Does the analysis provide sufficient…

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

Use the following for the next 2 questions. In a recent student survey, males and females were
asked “At what age do you expect to retire?” Assume the students who responded to the
survey represent an SRS of all undergraduate students. Do males and females plan to retire at
the same age? A two-sample t-test was performed using MINITAB:
Descriptive Statistics: Retire
Gender N Mean StDev SE Mean
Female 391 63.26 8.06 0.41
Male 239 61.14 11.99 0.78
Estimation for Difference
95% CI for
Difference Difference
2.12 (0.396, 3.841)
Test
Null hypothesis H0 : μ1 − μ2 = 0
Alternative Hypothesis H1 : μ1 − μ2 6= 0
T-Value DF P-Value
2.418 370.21 0.016
42. Does the analysis provide sufficient evidence at the significance level α = 0.05 to conclude
that, on the average, females and males plan to retire at different ages? Why?
(A) No, since the p-value = 0.016 is less than α = 0.05 we fail to reject H0 and conclude that
females and males plan to retire about the same age.
(B) No, there is weak evidence that the retirement ages are different since the p-value is small.
(C) Yes, there is strong evidence since the mean retirement ages for females and males are
63.26 and 61.14, respectively.
(D) Yes, there is both practical significance and statistical significance to suggest that all males
will retire at an older age than females will.

(E) Yes, there is evidence (p-value = 0.016) that, on average, females and males plan to retire at

different ages.

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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