Answered: x is a random variable. It has a…

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

x is a random variable. It has a distribution that is approximately normal with population mean of about 14. There are 10 data points as follows:

15, 18, 17, 18, 15, 13, 14, 16, 17, 10

Does the information indicate that the population average is higher tihan 14? Use alpha=0.01

State the null and alternate hypotheses. What sampling distribution will you use?

Estimate the P value.

Expert Solution

Step 1

Null Hypothesis:

H0: The population average is not higher than 14.

Alternative Hypothesis:

H1: The population average is higher than 14.

In the given situation, the population standard deviation is not known and the sample size is less than 30.

Hence, we use t sampling distribution.

Test statistic:

For the given data values,

$\bar{x} = 15.3, f r o m t h e e x c e l f u n c t i o n, = A V E R A G E (M 2 : M 11) s = 2.4967, f r o m t h e e x c e l f u n c t i o n, = S T D E V . S (M 2 : M 11)$

$t = \frac{\bar{x} - μ}{\frac{s}{\sqrt{n}}} = \frac{15.3 - 14}{\frac{2.4967}{\sqrt{10}}} = 1.6466$

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