Question

From her firm's computer telephone log, an executive found that the mean length of 60 telephone calls during July was 4.54 minutes with a standard deviation of 5.07 minutes. She vowed to make an effort to reduce the length of calls. The August phone log showed 42 telephone calls whose mean was 2.408 minutes with a standard deviation of 2.293 minutes.

(a)	Choose the appropriate hypotheses assuming the desire to reduce the length of calls. Assume µ1 is the average call length in July and µ2 is the average call length in August.
	a. H0: μ1 – μ2 ≤ 0 vs. H1: μ1 – μ2 > 0
	b. H0: μ1 – μ2 ≥ 0 vs. H1: μ1 – μ2 < 0
	a b

(b-1)

Obtain a test statistic tcalc and p-value assuming unequal variances. (Round your answers to 3 decimal places.)

tcalc
p-value

(b-2)

Interpret the results using α = .01.

(Click to select)Do not rejectReject the null hypothesis.

(b-3)

What is your conclusion at α = .01?

  

We (Click to select)cannotcan conclude the length of calls had been reduced.

Answer 1

(a) The Hypothesis is Option a:

H0: =

Ha: <

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(b-1) The Test Statistic:

The p Value:    The p value (Left tail) for t = 2.865, df = 88 (calculated below), is; p value = 0.0026

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(b-2) Since p value is < 0.01, Reject H0.

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(b-3) We can conclude that the length of calls has been reduced

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The Degrees of Freedom

Since we are considering unequal variances, we calculate the degrees of freedom as given below.