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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Step 1- Given Information

Solution:

We have given that,

Let X1 be a random variable having male BMI 

      X2 be a random variable with female BMI

Statistics homework question answer, step 1, image 1

Statistics homework question answer, step 1, image 2

Statistics homework question answer, step 1, image 3

Note: Do not assume population standard deviation are equal.

 

Step 2- Testing of hypothesis (Formulae and computations )

Part a)

We have to test the claim that males and females have same Body Mass Index (BMI)

Null hypothesis (H0) is hypothesis of "no difference".

Statistics homework question answer, step 2, image 1

Alternative hypothesis (H1) is opposite of null hypothesis.

Statistics homework question answer, step 2, image 2

The null and alternative hypothesis is given by,

Statistics homework question answer, step 2, image 3

 

Formula for test statistic :

Statistics homework question answer, step 2, image 4

Plugging values in formula, we get

Statistics homework question answer, step 2, image 5

Statistics homework question answer, step 2, image 6

The test statistic, t = 2.11

 

Formula for degrees of freedom is,

Statistics homework question answer, step 2, image 7

Plugging values in formula, we get

Statistics homework question answer, step 2, image 8

Statistics homework question answer, step 2, image 9

P-value :

Using t table, P-value is given by

P-value = 0.038                                     (or using excel command , =T.DIST.2T(2.11,72.58) = 0.038)

 

Decision rule and conclusion :

Statistics homework question answer, step 2, image 10

Here, P-value=0.038 > 0.05 so  fail to reject Ho

Conclusion :

Fail to reject the null hypothesis , there is not sufficient evidence to warrant rejection of claim that men and women have same BMI.

 

 

 

 

 

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