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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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Please help me with the steps in statcrunch:

Think about a population mean that you may be interested in and propose a hypothesis test problem for this parameter. you may believe that the population mean number of times that adults gas up their vehicles each week is less than 2.5. data could be that you spoke with 7 people and found that they went out 2, 3, 1, 4, 2, 1, and 5 times last week. You then would choose to test this hypothesis at the .05 (or another) significance level. Assume a random sample.

Expert Solution

Step 1

For the given problem, the population mean $(μ)$ is 2.5.

The data(sample) is said to be on 7 people i.e. n=7.

The sample mean is the average of the sample. Thus,

sample mean $(\bar{x)}$ = $\frac{2 + 3 + 1 + 4 + 2 + 1 + 5}{7}$

=2.57

The standard deviation $(σ)$ of the sample is $\sqrt{\frac{1}{n} \underset{i}{\sum (} x i - {\bar{x)}}^{2}}$

= $\sqrt{\frac{1}{7} [{(2 - 2.57)}^{2} + {(3 - 2.57)}^{2} + {(1 - 2.57)}^{2} + {(4 - 2.57)}^{2} + {(2 - 2.57)}^{2} + {(1 - 2.57)}^{2} + {(5 - 2.57)}^{2}]}$

=( $\sqrt{\frac{1}{7} (0.3249 + 0.1849 + 2.4649 + 2.0449 + 0.3249 + 2.4649 + 5.9049}$ )

=1.3995

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