Researchers are interested in determining if the average cgo

Researchers are interested in determining if the average cgolesterol level of offspring of men who died of heart disease is elevated above normal. Suppose it is known that the mean cholesterol level in children is 175mg/ml. It is further assumed that levels are normally distributed with = 50 mg/ml. A group of 10 children whose fathers have died from heart disease were found to have a mean of 200 mg/ml

a) Test at the .01 significance that the mean cholesterol is higher in this group than the general poulation.

b) Determine the p-value for this test.

Solution

A)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   175  
Ha:    u   >   175  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha =    0.01          
zcrit =    +   2.326347874      
              
Getting the test statistic, as              
              
X = sample mean =    200          
uo = hypothesized mean =    175          
n = sample size =    10          
s = standard deviation =    50          
              
Thus, z = (X - uo) * sqrt(n) / s =    1.58113883          
              
Also, the p value is              
              
p =    0.056923149          
              
Comparing z and zcrit (or, p and significance level), we   FAIL TO REJECT THE NULL HYPOTHESIS.          
Thus, there is no significant evidence that the mean cholesterol is higher in this group than the general poulation. [CONCLUSION]

b)

As already said, using technology,

p = .056923149 [answer]