Question

Problem 1

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. Samples of 20 problems reported to two different offices of a telecommunications company and the time to clear those problems (in minutes) from the customers’ lines.

Data summary table:

Problem 1 data
Mean 1	2.21
Mean 2	2.01
Std. Dev. 1	1.72
Std. Dev. 2	1.89

Using the output below answer the answer the flowing questions:

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	20
Sample Mean	2.21
Sample Standard Deviation	1.72
Population 2 Sample
Sample Size	20
Sample Mean	2.01
Sample Standard Deviation	1.89
Intermediate Calculations
Population 1 Sample Degrees of Freedom	19
Population 2 Sample Degrees of Freedom	19
Total Degrees of Freedom	38
Pooled Variance	3.2653
Standard Error	0.5714
Difference in Sample Means	0.2000
t Test Statistic	0.3500
Two-Tail Test
Lower Critical Value	-2.0244
Upper Critical Value	2.0244
p-Value	0.7283

Assuming the population variances are unknown but equal, to test if (at level of significance .05) there is any significant difference between the mean waiting time between the two offices?,

a) What is the null hypothesis?

b) What is the correct t-statistic?

c) What is the correct decision rule?

d) What is the correct conclusion?

e) Using only the p-value in the Excel output for problem 1, can it be concluded that there is any significant difference between the mean waiting time of the 2 groups at level of significance =.1?

f) If in fact the true means were significantly different, based on the correct conclusion for Problem 1, would an error be made?

Answer 1

(a) There is no difference between the mean waiting time between the two offices.

(b) The correct t-statistic is 0.3500.

(c) Reject Ho if t > 2.0244 or t < -2.0244.

(d) Fail to reject Ho and conclude that there is no difference between the mean waiting time between the two offices.

(e) Since the p-value (0.7283) is greater than the significance level (0.10), we fail to reject the null hypothesis.

Conclude that there is no difference between the mean waiting time between the two offices.

(f) Type II error