Chicken Feed A farmer fed different diets to two groups of 1

Chicken Feed: A farmer fed different diets to two groups of 100 chicks each. Assume that all factors other than the diets have been kept equivalent for the two groups. For those chicks fed diet A, the average weight gain in two weeks, for those chicks that survived, was 25 ounces with a standard deviation of 5 ounces, however, 13 chicks died during the period. For those fed diet B, the average weight gain in two weeks, again for those chicks which survived, was only 15 ounces with a standard deviation of 4 ounces, but only 7 chicks died. Using this data, answer the following questions Question 1 Assuming that the true variation in weight gain is the same for both diets (i.e., assuming homoscedasticity) find a 95% confidence interval for muA - muB, the difference in average weight gain between diet A and diet B, for chicks which survive.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   24  
Ha:    u   >   24  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    +   1.644853627      
              
Getting the test statistic, as              
              
X = sample mean =    25          
uo = hypothesized mean =    24          
n = sample size =    100          
s = standard deviation =    5          
              
Thus, z = (X - uo) * sqrt(n) / s =    2          
              
Also, the p value is              
              
p =    0.022750132          
              
Comparing z and zcrit (or, p and significance level), we   REJECT THE NULL HYPOTHESIS.          
              
Thus, there is significant evidence to claim that the weight gain is more than 24 ounces. [CONCLUSION]