Studies in the general population suggest that the gestation

Studies in the general population suggest that the gestation length of uncomplicated pregnancies varies according to a normal distribution with u=39 weeks with o=2 weeks. A sample of 22 middle-class African American women demonstrates an average gestation length (x)[mean] of 38.5 weeks. test whether the mean gestation period in the african american women is significantly different from the expected value of 39 weeks. use a two-sided alternative hypothesis. show all hypothesis steps.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   39  
Ha:    u   =/   39  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    21          
tcrit =    +/-   2.079613845      
              
Getting the test statistic, as              
              
X = sample mean =    38.5          
uo = hypothesized mean =    39          
n = sample size =    22          
s = standard deviation =    2          
              
Thus, t = (X - uo) * sqrt(n) / s =    -1.17260394          
              
Also, the p value is              
              
p =    0.254085212          
              
As |t| < 2.0796, or P > 0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.          
              
Thus, there is no significant evidence to say that the sample of African American women has a mean gestation period different from 39 weeks. [CONCLUSION]