A nurse claims that the variations of the lengths of newborn males is different

Question

A nurse claims that the variations of the lengths of newborn males is different from the variations of the lengths of newborn females. A sample of 10 newborn males is selected and the standard deviation is 1.9 inches. The standard deviation of a sample of 11 newborn females is 0.9 inch. Testing the nurse's claim at a = 0.05 which of the following NOT correct?

a. The critical value is 3.78.

b. The critical value is 3.02.

c. Reject the null hypothesis.

d. There is enough evidence to support the claim.

Explanation / Answer

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    two   tailed test.      
              
Thus, getting the critical F, as alpha =    0.05   ,      
alpha/2 =    0.025          
df1 = n1 - 1 =    9         
df2 = n2 - 1 =    10          
F (crit) =    0.252279016   and   3.778962634 [or 3.78]
              
Getting the test statistic, as              
s1 =    1.9          
s2 =    0.9          
              
Thus, F = s1^2/s2^2 =    4.456790123          
              
As F is not between the two critical values, we REJECT THE NULL HYPOTHESIS.              

Hence, as we see, only

OPTION B: b. The critical value is 3.02. [ANSWER, B]

is not correct.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.