The resistances of a certain type of thermistor are specified to be normally dis

Question

The resistances of a certain type of thermistor are specified to be normally distributed with a mean of 10, 000 ohms and a standard deviation of 500 ohms, at a temperature of 25oC. Thus, only about 2.3% of these thermistors should produce resistances in excess of 11, 000 ohms. The exact measurement of resistances produced is time-consuming, but it is easy to determine whether the resistance is larger than a specified value (say, 11, 000). For 100 thermistors tested, 5 showed resistances in excess of 11, 000 ohms. Do you think the thermistors from which this sample was selected fail to meet the specifications? Why or why not?

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Explanation / Answer

Data:    

n = 100   

p = 0.023   

p' = 0.05   

Hypotheses:   

Ho: p 0.023   

Ha: p > 0.023   

Decision Rule:   

= 0.05   

Critical z- score = 1.644853627

Reject Ho if z > 1.644853627

Test Statistic:   

SE = {(p (1 - p)/n} = (0.023 * (1 - 0.023)/100) = 0.01499033

z = (p' - p)/SE = (0.05 - 0.023)/0.0149903302165096 = 1.801161123

p- value = 0.0358387   

Decision (in terms of the hypotheses):

Since 1.8011611 > 1.644853627 we reject Ho

Conclusion (in terms of the problem):

The proportion if failing thermistors is more than 2.3%

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