Question

5. Inferential Statistics - Hypothesis Testing Historically, evening long-distance calls from a particular city have averaged 16.2 minutes per call. In a random sample of 41 calls, the sample mean time was 17.8 minutes. Assume the (sample) standard deviation is known to be 6 minutes. Using 0.05 level of significance, is there sufficient evidence to conclude that the average evening long-distance call has increased? Explain through the use of a one-tailed test (as in examples in the notes).

Answer 1

Answer:

sample size = 41

sample mean = 17.8

standard deviayion = 6

Alpha = 0.05

hypothesis test:

H0 : mu = 16.2

Ha : mu < 16.2

Zcritical value = 1.645

test statistic:

Z = X - mu/(s/sqrt n)

= 17.8 - 16.2 / 6/sqrt (41)

= 17.8-16.2/0.937

= 1.6/0.937 =1.707

Z > Zcritical value

we fail to reject the null hypothesis.

there is not suficient evidence the average evening long lasting call has increased