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.
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