Sample after calibration:     mean  is  95.8   ,     SD  is   4.9     and sample size is 10 Sample before calibration:       mean  is  89.352   ,     SD  is   4.2      and sample size is 62 We do not know population standard deviations.   What is the p-value?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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A scale is known to be "low-calibrated" in that it measures an aluminum bar to be 4 grams lower than the actual weight.   If ????μold is the mean of all possible measurements of the bar using the old calibration,   and  ????μnew is the mean of all possible measurements of the bar using a re-calibrated scale.  It is desired that     ????−????=4μnew−μold=4.

 

 

Consider the test

          ?0:????−????=4H0:μnew−μold=4   vs.  ?0:????−????≠4H0:μnew−μold≠4 

 

 

 

Sample after calibration:     mean  is  95.8   ,     SD  is   4.9     and sample size is 10

Sample before calibration:       mean  is  89.352   ,     SD  is   4.2      and sample size is 62

We do not know population standard deviations.

 

What is the p-value?       (Hint:  best to use software, or else the Desmos Calculator for the 2 sample T and Z test)

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