# Aj Davis Case Study Solution

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INTRODUCTION In business field, there are many uncertain situations business owners and managers would face. In order to make a decision about their businesses, the managers need analyzed information, which could be provided by statistic method.
AJ Davis department store, a chain store, wants to analysis the credit customers so the sample data of 50 credit customers was collected. The manager at the store has speculated some information about credit customers. By using the sample data of 50 credit customers, along with hypothesis testing and confidence intervals, we could determine whether manager’s speculations are convincing. Also, this report provides the summarization on the four variables of interests; income, location, number of years
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The test of hypothesis at 0.05 significant levels and the determination of 95% confidence intervals are performed to evaluate the validity of the manager’s speculations. The results are reported in the following part.
Speculation A: The average (mean) annual income is less than \$50,000.
According to the statistical analysis of 50 sample customers, we can assume that the average annual income of the store credit customer is less than \$50,000. The sample mean of 50 customers is \$43,740 with sample standard deviation \$14,640. By estimating the determined confidence interval (see Appendix A), we can be 95% confident that the average annual income lies within the interval of \$39,580 and \$47,900. As the upper limit is less than \$50,000, it obviously supports the manager’s claim. In addition, the result of hypothesis test, both observed z-value and p-value, rejected the null hypothesis that the average income equals to \$50,000. Therefore, we agree that the average annual income is less than
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According to the given sample data of 50 customers, there are 15 credit customers who live in suburban area with the sample mean of credit balance \$4,675, and the sample standard deviation at \$742. The result of statistical analysis in Appendix D shows that we can be 95% confident that the mean credit balance for suburban customers is between \$4,264 and \$5,086. As the lower limit of the interval is less than \$4,300, it not supports the manager’s claim. However, the result of hypothesis test rejects the null hypothesis, and provides convincing evidence that the mean credit balance for suburban customers is greater than \$4,300. Although these statistic methods contribute different conclusions, we agree with the outcome of hypothesis test because we used one-tailed test og hypothesis, which is consistent with the manager’s claim (explained in Appendix D). Therefore, we agree that the average of credit balance of suburban customers is more than

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