Question

1. Historically, evening long-distance phone calls from a particular city have averaged 12 minutes per call. In a random sample of 20 calls, the sample mean was 10.7 minutes per call, with a standard deviation of 4 minutes. Does the sample indicate that there has been a change in the mean duration of long distance phone calls? Test the appropriate hypothesis at the 10% level of significance. (Be sure to state the hypotheses and report your conclusion).                      [5 marks]
   
   
   
   
   
   
   
   
   

Part B: Estimate the p-value. Show how you came up with your answer.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 12
Alternative Hypothesis, Ha: μ ≠ 12

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (10.7 - 12)/(4/sqrt(20))
t = -1.453

P-value Approach
P-value = 0.1625 (Excel function: =2*T.DIST(-1.453,19,TRUE))

As P-value >= 0.1, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the mean has changed from 12