Statistics Question
Solution:
We have given that,
Let X1 be a random variable having male BMI
X2 be a random variable with female BMI
Note: Do not assume population standard deviation are equal.
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".
Alternative hypothesis (H1) is opposite of null hypothesis.
The null and alternative hypothesis is given by,
Formula for test statistic :
Plugging values in formula, we get
The test statistic, t = 2.11
Formula for degrees of freedom is,
Plugging values in formula, we get
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 :
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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