Question

Historically, evening long-distance calls from a particular city have averaged 15.2 minutes per call. In a random sample of 35 calls, the sample mean time was 14.3 minutes. Assume the standard deviation is known to be 5 minutes. Using a 0.05 level of significance, is there sufficient evidence to conclude that the average evening long-distance call has decreased? Note: Use the six-steps – clearly labeled (15 pts.)

1. State the null hypothesis and the alternative hypothesis
2. Determine the critical value(s); (draw graph)
3. State your decision rule
4. What statistic should be used to test the null hypothesis? Determine the test statistic:
5. What is the outcome/value calculated? Make a decision (reject or accept):
6. Decision based on the results of the statistical test? Draw a conclusion (in the context of the problem):

Answer 1

Here null hypothesis

and aternate hypothesis

As n is greater than 30 and standard deviation is given we will use z distribution

We will find test statistic

First we will find z

Now P-value =P(z<-1.065)=0.1434

As P-value is greater than alpha=0.05 we we fail to reject the null hypothesis.

So there is no sufficient evidence to support the claim that the average evening long-distance call has decreased.

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