Question

Blood glucose levels for obese patients have a mean of 100 with a standard deviation of 20. A researcher thinks that a diet high in protein will have a positive or negative effect on blood glucose levels. A sample of 30 obese patients who have tried a high in protein diet have a mean glucose level of 96. Test the hypothesis that a diet high in protein has an effect blood glucose using a z-test with a level of significance =.035

Answer 1

Ho :   µ =   100  
Ha :   µ ╪   100   (Two tail test)
          
Level of Significance ,    α =    0.035  
population std dev ,    σ =    20.0000  
Sample Size ,   n =    30  
Sample Mean,    x̅ =   96.0000  
          
'   '   '  
          
Standard Error , SE = σ/√n =   20/√30=   3.6515  
Z-test statistic= (x̅ - µ )/SE =    (96-100)/3.6515=   -1.0954  
          
critical z value, z* =   ±   2.1084   [Excel formula =NORMSINV(α/no. of tails) ]
          
p-Value   =   0.2733   [ Excel formula =NORMSDIST(z) ]
Decision:   p-value>α, Do not reject null hypothesis       
Conclusion: There is not enough evidence to conclude that   a diet high in protein has an effect blood glucose