Question

Free Response: Answer each question completely, and show your work. 1. Nitrites are often added to meat products as preservatives. In a study of the effect of these chemicals on bacteria, the rate of uptake (in nanograms per second) of a radio-labeled amino acid was measured for a number of cultures of bacteria, some growing in a medium to which nitrites had been added randomly. Here are the summary statistics from this study Group Nitrite Contro.1 30 81121250 (a) Carry out a formal test of the research hypothesis that nitrites decrease amino acid uptake and interpret your results. Use a 5% level of significance. (b) Various replications of this type of experiment show that nitrates are effective in reducing the rate of amino acid uptake. Based on this information, what type of error was it posible to make in part (a)? Did you make that error? Explain.

Answer 1

(a)                  

Data:                        

n1 = 30                      

n2 = 30                      

x1-bar = 7880                      

x2-bar = 8112                      

s1 = 1115                      

s2 = 1250                      

Hypotheses:                       

Ho: μ1 ³ μ2                       

Ha: μ1 < μ2                       

Decision Rule:                       

α = 0.05                      

Degrees of freedom = 30 + 30 - 2 = 58                  

Critical t- score = -1.671552763                   

Reject Ho if t < -1.671552763                   

Test Statistic:                       

Pooled SD, s = √[{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] =      √(((30 - 1) * 1115^2 + (30 - 1) * 1250^2) / (30 + 30 - 2)) = 1184.424966      

SE = s * √{(1 /n1) + (1 /n2)} = 1184.4249659645 * √((1/30) + (1/30)) = 305.8172112               

t = (x1-bar -x2-bar)/SE = (7880 - 8112)/305.817211200852 = -0.758623097               

p- value = 0.225574969                     

Decision (in terms of the hypotheses):                    

Since -0.758623097 > -1.671552763 we fail to reject Ho              

Conclusion (in terms of the problem):                     

There is no sufficient evidence that nitrites decrease amino acid uptake                

(b) If replications of such experiments show that nitrites are effective in decreasing the amino acid uptake, we have failed to reject a false null hypothesis, thereby committing a type II error.