9.40 :The mean water temperature downstream from a power plant cooling tower dis

ID: 3152310 • Letter: 9

Question

9.40 :The mean water temperature downstream from a

power plant cooling tower discharge pipe should be no more

than 100°F. Past experience has indicated that the standard

deviation of temperature is 2°F. The water temperature is

measured on nine randomly chosen days, and the average

temperature is found to be 98°F.

(a) Is there evidence that the water temperature is acceptable

at alpha = 0.05?

(b) What is the P-value for this test?

at alpha= 0.05 if the water has a true mean temperature of

104°F

Answer to the question)

Claim : M < 100

Hypothesis:

Ho: M = 100

Ha: M < 100

Sample size n = 9

Population standard deviation s = 2

Sample mean x bar = 98

z = (x bar - M) / (s / sqrt(9))

z = (98 -100) / (2 /sqrt(9))

z = -3

P value for z = -3 is 0.00135

Inference: Since the P value .0.00135 < alpha 0.05 , we reject the null

Conclusion: Thus we state there is significant evidence to conclude that the temperature is less than 100

Part c)

the probabiltiy fo accepting the null if x bar = 104 can be calculated as follows

z = (104-100) / (2 / sqrt(9))

z = 6

P(z < 6) = 1

thus the probability is 1 for accepting the null if the sample mean temperature is 104

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