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 in an essay with a minimum of 500 words:

• 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

1)

Assumptions for independent samples t-test

a) Samples should follow normal distribution.

b) Equality for variances.

assumption for equal variances are not met. Hence we perform independent samples t-test with unequal variances.

1)

μ₁: mean of Uptown

µ₂: mean of Midtown

Difference: μ₁ - µ₂

Equal variances are not assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Uptown	66	10.78	2.76	0.34
Midtown	84	11.83	3.97	0.43

Estimation for Difference

Difference	95% CI for Difference
-1.045	(-2.133, 0.043)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
-1.90	145	0.060

Since p-value is more than alpha 0.05 we fail to reject null hypothesis and there is no significant evidence to conclude that there are differences between the amount of time it takes to resolve the calls by location.

2)

expected counts =

	Midtown	Uptown	Row Totals
Caller Verification	15  (13.62)	12  (13.38)	27
Provided Correct Information	17  (14.13)	11  (13.87)	28
Correct Update	14  (15.14)	16  (14.86)	30
Other Error Types	10  (13.12)	16  (12.88)	26
Column Totals	56	55	111  (Grand Total)

the values in () are expected counts.

Oij = Observed value of two nominal variables
Eij = Expected value of two nominal variables
Degree of freedom is calculated by using the following formula:
DF = (r-1)(c-1)
Where
DF = Degree of freedom
r = number of rows
c = number of columns

The chi-square statistic is 3.1282.

df = 3

The p-value is 0.372272.

Since p-value is more than alpha 0.05 we fail to reject null hypothesis and conclude that error type and location are independent of each other.