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? **Use the six-steps
(clearly labeled )**

Answer #1

Solution:

1)

The null and alternative hypothesis are

**H0 :
= 15.2 vs Ha :
< 15.2**

2)

Test statistic z = = [14.3- 15.2]/[5/35] = -1.06

**Test statistic z = -1.06**

3)

Given , 0.05 level of significance,

Here , left tailed test

So , critical value is

Critical value is -1.65

Rejection rule : Reject H_{0} if z < -1.65

4)

**p value = P(Z < -1.06) = 0.1446**

5)

**Decision : Fail to reject H _{0}**

Because p value is greater than 0.05 level of significance,

6)

**Conclusion: There is not sufficient evidence to conclude
that the average evening long-distance call has
decreased**

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