Question

Using the Sample Hypothesis Test Data and Chi-Square Data with a .05 level of significance, provide a summary report for the Vice President including the following information:

• Two-Sample Hypothesis Test: Discuss the hypothesis test assumptions and test used. Provide the test statistic and p-value in your response. Evaluate the results of the hypothesis test with the scenario. Provide recommendations for the Vice President.
• Chi-square Hypothesis Test: Discuss the hypothesis test assumptions and test used. Provide the test statistic and p-value in your response. Evaluate the results of the hypothesis test with the scenario. Provide recommendations for the Vice President.

Scenario

Land and Agua Insurance company has a call center in the Tempe, Arizona. The business was originally established in Phoenix, Arizona in 1972 as a small business and has grown with the population of the city.   The insurance company specialized in bundling cars, off-road vehicles and watercraft such as jet skis and boats. The company has 150,000 clients in Arizona.

Marjorie Jones, Vice President of Operations is concerned with both the customer complaints and the amount of time representatives are taking to resolve the calls. The team is focused on two areas from the project data collection: call time by location and error type by location. The Vice President wants to know if there is a difference in the amount of time it takes to resolve the calls by location; and a relationship between error type and location.

Team	Call Time
Uptown	6.67
Uptown	6.67
Uptown	6.67
Uptown	6.67
Uptown	7.18
Uptown	7.18
Uptown	7.18
Uptown	7.18
Uptown	7.18
Uptown	8.21
Uptown	8.21
Uptown	8.72
Uptown	8.72
Uptown	9.23
Uptown	9.23
Uptown	9.23
Uptown	9.23
Uptown	9.76
Uptown	9.76
Uptown	10.27
Uptown	10.27
Uptown	10.27
Uptown	10.27
Uptown	10.27
Uptown	10.78
Uptown	10.78
Uptown	10.78
Uptown	10.78
Uptown	10.78
Uptown	10.78
Uptown	10.78
Uptown	10.78
Uptown	10.78
Uptown	11.81
Uptown	11.81
Uptown	11.81
Uptown	12.32
Uptown	12.32
Uptown	12.32
Uptown	12.32
Uptown	12.84
Uptown	12.84
Uptown	13.35
Uptown	13.35
Uptown	13.86
Uptown	15.92
Uptown	16.43
Uptown	16.95
Uptown	17.46
Uptown	21.00
Uptown	6.16
Uptown	9.23
Uptown	9.75
Uptown	9.84
Uptown	9.99
Uptown	10.23
Uptown	10.55
Uptown	11.11
Uptown	11.29
Uptown	11.29
Uptown	11.80
Uptown	11.80
Uptown	11.80
Uptown	12.32
Uptown	12.32
Uptown	12.32
Midtown	12.32
Midtown	12.32
Midtown	12.32
Midtown	12.32
Midtown	12.84
Midtown	12.84
Midtown	12.84
Midtown	12.84
Midtown	13.35
Midtown	13.35
Midtown	13.86
Midtown	13.86
Midtown	14.38
Midtown	14.38
Midtown	14.38
Midtown	14.38
Midtown	14.38
Midtown	14.89
Midtown	14.89
Midtown	14.89
Midtown	15.41
Midtown	15.41
Midtown	15.92
Midtown	16.43
Midtown	16.95
Midtown	17.46
Midtown	17.97
Midtown	18.49
Midtown	18.49
Midtown	18.49
Midtown	19.00
Midtown	19.51
Midtown	20.03
Midtown	20.03
Midtown	5.39
Midtown	5.39
Midtown	5.39
Midtown	5.39
Midtown	5.91
Midtown	5.91
Midtown	5.91
Midtown	5.91
Midtown	5.91
Midtown	6.93
Midtown	6.93
Midtown	7.45
Midtown	7.45
Midtown	7.96
Midtown	7.96
Midtown	7.96
Midtown	7.96
Midtown	8.47
Midtown	8.47
Midtown	8.47
Midtown	8.99
Midtown	8.99
Midtown	8.99
Midtown	8.99
Midtown	8.99
Midtown	9.50
Midtown	9.50
Midtown	9.50
Midtown	9.50
Midtown	9.50
Midtown	9.50
Midtown	9.50
Midtown	9.50
Midtown	10.53
Midtown	10.53
Midtown	10.53
Midtown	11.04
Midtown	11.04
Midtown	11.04
Midtown	11.04
Midtown	11.55
Midtown	11.55
Midtown	12.07
Midtown	12.07
Midtown	12.58
Midtown	14.63
Midtown	15.15
Midtown	15.66
Midtown	16.18
Midtown	17.20

	Location
Error Type	Midtown	Uptown	Total
Caller Verification	15	12	27
Provided Correct Information	17	11	28
Correct Update	14	16	30
Other Error Types	10	16	26
Total	56	55	111

Answer 1

Let represent uptown and midtown locations.

For testing the difference between call times by location we will use a two-sided t-test for population means.

Uptown	Midtown
6.67	12.32
6.67	12.32
6.67	12.32
6.67	12.32
7.18	12.84
7.18	12.84
7.18	12.84
7.18	12.84
7.18	13.35
8.21	13.35
8.21	13.86
8.72	13.86
8.72	14.38
9.23	14.38
9.23	14.38
9.23	14.38
9.23	14.38
9.76	14.89
9.76	14.89
10.27	14.89
10.27	15.41
10.27	15.41
10.27	15.92
10.27	16.43
10.78	16.95
10.78	17.46
10.78	17.97
10.78	18.49
10.78	18.49
10.78	18.49
10.78	19
10.78	19.51
10.78	20.03
11.81	20.03
11.81	5.39
11.81	5.39
12.32	5.39
12.32	5.39
12.32	5.91
12.32	5.91
12.84	5.91
12.84	5.91
13.35	5.91
13.35	6.93
13.86	6.93
15.92	7.45
16.43	7.45
16.95	7.96
17.46	7.96
21	7.96
6.16	7.96
9.23	8.47
9.75	8.47
9.84	8.47
9.99	8.99
10.23	8.99
10.55	8.99
11.11	8.99
11.29	8.99
11.29	9.5
11.8	9.5
11.8	9.5
11.8	9.5
12.32	9.5
12.32	9.5
12.32	9.5
	9.5
	10.53
	10.53
	10.53
	11.04
	11.04
	11.04
	11.04
	11.55
	11.55
	12.07
	12.07
	12.58
	14.63
	15.15
	15.66
	16.18
	17.2

: There is no difference between call times for diff locations ()

VS

: There is difference between call times for diff locations ()

Test Statistic :

Where = 66 = 84

=

= 3.4915

Test Stat =

= -1.820

p-value = 2* P ( < -1.820)

= 2 * P ( > 1.820)

= 0.071 Found using t distribution tables

Since p-value > 0.05

We have insufficient evidence to reject null hypothesis at 5% level. We conclude that there is no difference between the mean call times of locations.

For checking the relationship between error type and location. We are going to use a chi-square test of independence.

There is no relationship between error type and location.

VS

There is a relationship between error type and location.

Test Statistic:

Where Oi and Ei are observed and expected values. The observed are given in the question. We can calculate the expected using the folllowig example.

Eg. Expected for midtown and caller verification cell = =

	Location
Error Type	Midtown	Uptown	Total
Caller Verification	13.622	13.378	27
Provided Correct Information	14.126	13.874	28
Correct Update	15.135	14.865	30
Other Error Types	13.117	12.883	26
Total	56	55	111

Individual

	Location
Error Type	Midtown	Uptown
Caller Verification	0.139	0.142
Provided Correct Information	0.585	0.595
Correct Update	0.085	0.087
Other Error Types	0.741	0.754

Test Stat = 3.128

p-value at 0.05 and r (rows) = 4 and c = 2

p-value =

= 0.37

Since p-value > 0.05

There is insufficient evidence to reject the null hypothesis at 5% level of significance. We conclude that there is not relationship between error type and location.