Question

Sixteen laboratory animals were fed a special diet from birth through age 12 weeks. Their

weight gain (in grams) were as follows:

63 68 79 65 64 63 65 64 76 74 66 66 67 73 69 76

Can we conclude from these data that the diet results in a mean weight gain of less than 70

grams? Let α = 0.05.

Note: There are two possible ways to analyze this data. Use the statistical procedure

that makes use of the magnitudes of the differences between measures and a

hypothesized location parameter rather than just the signs of the differences.

Answer 1

Ho :   µ =   70                  
Ha :   µ <   70       (Left tail test)          
                          
Level of Significance ,    α =    0.05                  
sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   5.2520                  
Sample Size ,   n =    16                  
Sample Mean,    x̅ = ΣX/n =    68.6250                  
                          
degree of freedom=   DF=n-1=   15                  
                          
Standard Error , SE = s/√n =   5.2520   / √    16   =   1.3130      
t-test statistic= (x̅ - µ )/SE = (   68.625   -   70   ) /    1.3130   =   -1.05
                          
  
                          
p-Value   =   0.1558   [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value>α, Do not reject null hypothesis

conclusion : we can not conclude from these data that the diet results in a mean weight gain of less than 70 grams