Math 533: Applied Managerial StatisticsCourse Project B

Introduction

AJ Davis is a department store chain, which has several credit customers and want to find out more information about these customers.

The following report presents the detailed statistical analysis of the data collected from a sample of credit customers in the department chain store AJ DAVIS.

AJ Davis has complied a sample of fifty (50) credit customers with data selected in the following variables: Location, Income (in $1,000s), Size (Number of people living in the household), Years (number of years the customer has lived in the current location), and Credit Balance (customers current credit card balance on the stores credit car, in $).

The manager at AJ Davis has speculated the following:

The average (mean) annual income was less than $50,000.

The true population proportion of customers who live in an urban area exceeds 40%

The average (mean) number of years lived in the current home is less than 13 years

The average (mean) credit balance for suburban customers is less than $4300

I will analyze the speculated data listed above by performing hypothesis test for each of the above situations (using the Seven elements of a Test Hypothesis with a=.05) in order to see if there is evidence to support my managers beliefs in each case (a-d), explain my conclusion in simple terms, compute the p-value with the interpretation, follow up with computing 95% confidence intervals for each of the variables described in a. to d. along with interpreting these intervals. This paper will also include an Appendix with all the steps in hypothesis testing, as well as the confidence intervals and Minitab output

In order to understand how hypothesis testing is done it is important that you know the elements of the Test of Hypothesis, and what each step means.

The Seven elements of a Test of Hypothesis are:

invalid Hypothesis - A theory about the specific values of one or more population parameters. The theory generally represents the status quo, and we accept it until proven false.

Alternative (research) hypothesis (Ha)- A theory about the specific values of one or more population parameters. The theory generally represents the status quo, and we accept it until proven false

Test statistic - A sample statistic used to decide whether to reject the invalid hypothesis.

Rejection Region - The numerical values of the test statistic for which the invalid hypothesis will be rejected.

Assumptions- Clear statements of any assumptions made about the populations being sampled.

Experiment and calculation of test statistics- Performance of the sampling experiment and determination of the numerical value of the test statistic.

Conclusion-

a. If the numerical value of the test statistic falls in the rejection region then we reject the invalid hypothesis and conclude that the alternative is true.

b. If the test statistic does not fall in the rejection region, then we do not reject H0 as we have insufficient data to do so.

The average (mean) annual income was less than $50,000

I found that the average annual incomes are 43.74 or $46,060, and the standard deviation to be 14.64 or $14.064.

Set up Hypothesis Test

Ho: =50 H1: 0.4

95% Lower

Sample X N Sample p Bound Z-Value P-Value

1 22 50 0.440000 0.324532 0.58 0.282

Test and CI for One Proportion

Sample X N Sample p 95% CI

1 22 50 0.440000 (0.302411, 0.577589)

c. The average (mean) number of years lived in the current home is less than 13 years

Descriptive Statistics: Years

Variable Mean StDev Minimum Maximum

Years 12.260 5.086 1.000 20.000

One-Sample Z: Years

Test of mu = 13 vs < 13

The assumed standard deviation = 5.086

95% Upper

Variable N Mean StDev SE Mean Bound Z P

Years 50 12.260 5.086 0.719 13.443 -1.03 0.152

d. The average (mean) credit balance for suburban customers is less than $4300Descriptive Statistics: Credit Balance($)

Variable Mean StDev Minimum Maximum

Credit Balance($) 3970 933.49 1864 5678

One-Sample Z: Credit Balance($)

Test of mu = 4300 vs > 4300

The assumed standard deviation = 933.49

95%

Lower

Variable N Mean StDev SE Mean Bound Z P

Credit Balance($) 50 3970 933.49 132 3754 -2.50 0.994