Directions: For the following question, test the indicated claim about the varia

Question

Directions: For the following question, test the indicated claim about the variances or standard deviations of two populations. Assume that both samples are independent simple random samples from populations having normal distributions. A random sample of 16 women resulted in blood pressure levels with a standard deviation of 23 mmHg. A random sample of 17 men resulted in blood pressure levels with a standard deviation of 19.2 mmHg. Use a 0.05 significance level to test the claim that blood pressure levels for women vary more than blood pressure levels for men. Note: I can't use minitab, R or Excel can be used instead

Explanation / Answer

Let

sigma1 = population standard deviation for women
sigma2 = population standard deviation for men

Formulating the null and alternative hypotheses,              
              
Ho:   sigma1^2 / sigma2^2   <=   1  
Ha:    sigma1^2 / sigma2^2   >   1  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical F, as alpha =    0.05   ,      
alpha =    0.05          
df1 = n1 - 1 =    15         
df2 = n2 - 1 =    16          
F (crit) = 2.352222763     

[You can use =F.INV.RT(0.05,15,16) to get the critical F here.]
              
Getting the test statistic, as              
s1 =    23          
s2 =    19.2          
              
Thus, F = s1^2/s2^2 =    1.43500434          

As F < 2.3522, we fail to reject Ho.

Hence, there is no significant evidence at 0.05 level that blood pressure levels for women vary more than blood pressure levels for men. [CONCLUSION]

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