Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

The following measurements on blood viscosity were made on laboratory mice: 3.29

ID: 3225590 • Letter: T

Question

The following measurements on blood viscosity were made on laboratory mice: 3.29, 3.91, 4.64, 3.55, 3.57, 4.18, 3.74, 3.03, 4.81, 3.84 (a) One scientist strongly believes that the laboratory mice blood viscosity could not be different from the reference value, 3.55 with standard deviation 0.3. Is the sample mean different from the reference value using Bayesian approach? (b) His colleague thinks that the laboratory mice blood viscosity could be significantly influenced by environmental conditions providing an average value of 4.1 with standard deviation 0.3. Is the sample mean different from the reference value using Bayesian approach? All requirements are satisfied. Use alpha = 0.1.

Explanation / Answer

(a0

Data:     

n = 10    

= 3.55    

s = 0.3    

x-bar = 3.856    

Hypotheses:    

Ho: = 3.55    

Ha: 3.55    

Decision Rule:    

= 0.1    

Lower Critical z- score = -1.644853627   

Upper Critical z- score = 1.644853627   

Reject Ho if |z| > 1.644853627   

Test Statistic:    

SE = s/n = 0.3/10 = 0.09486833   

z = (x-bar - )/SE = (3.856 - 3.55)/0.0948683298050514 = 3.225523213

p- value = 0.001257426    

Decision (in terms of the hypotheses):   

Since 3.225523213 > 1.644853627 we reject Ho and accept Ha

Conclusion (in terms of the problem):   

There is sufficient evidence that the sample mean is different from the reference value

(b)

Data:     

n = 10    

= 4.1    

s = 0.3    

x-bar = 3.856    

Hypotheses:    

Ho: = 4.1    

Ha: 4.1    

Decision Rule:    

= 0.1    

Lower Critical z- score = -1.644853627   

Upper Critical z- score = 1.644853627   

Reject Ho if |z| > 1.644853627   

Test Statistic:    

SE = s/n = 0.3/10 = 0.09486833   

z = (x-bar - )/SE = (3.856 - 4.1)/0.0948683298050514 = -2.57198583

p- value = 0.010111703    

Decision (in terms of the hypotheses):   

Since 2.57198583 > 1.644853627 we reject Ho and accept Ha

Conclusion (in terms of the problem):   

There is sufficient evidence that the sample mean is different from the reference value.