Question

A problem with a phone line that prevents a customer from receiving or making calls is upsetting to both the customer and the telecommunications company. The following data sets contain samples I have 20 problems reported to two different offices of a telecommunications company and the time to clear these problems (in minutes) from the customers lines:

Central Office 1 time to clear problems (minutes):

1.48 1.75 0.78 2.85 0.52 1.60 4.15 3.97 1.48 3.10

1.02 0.53 0.93 1.60 0.80 1.05 6.32 3.93 5.45 0.97

Central Office 2 time to clear problems (minutes):

7.55 3.75 0.10 1.10 0.60 0.52 3.30 2.10 0.58 4.02

3.75 0.65 1.92 0.60 1.53 4.23 0.08 1.48 1.65 0.72

A. Assuming that the population variances from both offices are equal, is there evidence of a difference in the mean waiting time between the two offices? (Use a = 0.05).

B. Find the p-value in (a) and interpret its meaning.

C. What other assumptions is necessary in (a)?

D. Assuming that the population variances from both offices are equal, construct and interpret a 95% confidence interval estimate of the difference between the population means in the two offices.

Answer 1

Using Excel<data<megastat<Hypothesis Test<Two independent groups<pooled<Two tailed

Central Office 1	Central Office 2
2.2140	2.0115	mean
1.7180	1.8917	std. dev.
20	20	n
	38	df
	0.20250	difference (Central Office 1 - Central Office 2)
	3.26510	pooled variance
	1.80696	pooled std. dev.
	0.57141	standard error of difference
	0	hypothesized difference
	0.354	t
	.7250	p-value (two-tailed)
	-0.95426	confidence interval 95.% lower
	1.35926	confidence interval 95.% upper
	1.15676	margin of error

A. Assuming that the population variances from both offices are equal, is there evidence of a difference in the mean waiting time between the two offices? (Use a = 0.05).

From Above output:

T=0.354

Critical Value= 2.334

Since T <Critical Value, We fail to reject H0.

There is not sufficient evidence to conclude that difference in the mean waiting time between the two offices are different.

B. Find the p-value in (a) and interpret its meaning.

From Above output

P value=0.7250>alpha(0.05)

Since P value>alpha, We fail to reject the null hypothesis

There is not sufficient evidence to conclude that difference in the mean waiting time between the two offices are different.

Interpret

More than 73% of test results would provide stronger evidence for rejecting the equality of the means.

C. What other assumptions is necessary in (a)?

We that the  population follows the normal distribution

D. Assuming that the population variances from both offices are equal, construct, and interpret a 95% confidence interval estimate of the difference between the population means in the two offices.

The 95% confidence interval is (-0.9543,1.3593)

Interpretation:

We are 95% confident that the population mean difference will be within this interval.