The manager of a large company claims that the standard deviation of the time (i

Question

The manager of a large company claims that the standard deviation of the time (in minutes) that it takes a telephone call to be transferred to the correct office in her company is 1.8 minutes. A random sample of 15 calls is selected, and the calls are timed. The standard deviation of the sample is 1.2 minutes. At a = 0.01, test the claim that the standard deviation is less than 1.8 minutes. a) H_0: ____ (remember to identify claim) b) H_0: ____ H_1: ____ b) Critical Value = ____ c) Test Value = ____ d) Reject H_0 or do not reject H_0? ____ e) Summary sentence:

Explanation / Answer

Data:    

n = 15   

= 1.8   

s = 1.2   

Hypotheses:    

Ho: 1.8   

Ha: < 1.8 [This is the claim]

Decision Rule:    

Degrees of freedom = n - 1 =    15 - 1 = 14

= 0.05   

Critical value =   6.570631457

Reject Ho if the test 2 value <    6.570631457

Test Statistic:    

2 = (n - 1) s^2 / s^2 =   (15 - 1) * 1.2^2 / 1.8^2 = 6.222222222

p- value = 0.03942441   

Decision (in terms of the hypotheses):    

Since 6.222222222 < 6.570631457 we reject Ho

Conclusion (in terms of the problem):    

It appears that the population standard deviation is less than 1.8 minutes.

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