Statistics Question
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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Expert Solution
Step 1
a.
In this case, the population standard deviation is not given. The samples are used to obtain the sample mean and sample standard deviation.
Thus, t test should be used.
Step 2
b.
Denote μ as the population mean retirement age.
Null hypothesis:
H0: μ = 65 years.
Alternative hypothesis:
H1: μ > 65 years.
c.
The sample size is n = 15.
The sample mean is obtained as follows:
The sample standard deviation is obtained as follows:
The degrees of freedom (df) for a one-sample t-test, for a sample of size n is (n – 1). Here, n = 15, so that df = 14.
The test statistic is: t = (x̄ – μ) / (s/√n).
Here, the sample mean is x̄ = 70.067.
Thus,
t = (70.067 – 65) / (5.612/√15)
= 5.067/1.450
≈ 3.494.
The test statistic is 3.494.
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