Posted: October 4th, 2013
Case 2
Case 2
Using the same format for reporting as in Case 1 (Introduction, Analysis & Results), generate a case report that addresses the following instructions.
Instructions
You will be using the Unit 2.xlsx dataset to make probability statements and statistical inference. You will be using only the quantitative measures: Income (1000s), Household Size, Amount Charged ($), and Age.
Questions
1. Consider the variable Amount charged (quantitative).
a. Assume that the population of Amount Charged follows an approximately normal distribution. Use a population mean of 4000 and a population standard deviation of 900. What is the probability that a cardholder will charge more than $6000?
b. What is the probability that a cardholder will charge between $3000 and $5000?
c. The middle 95% of cardholders will charge between what min and max?
d. There is one low amount charged. Is it so low that we would call it an outlier? Use a probability to support your answer.
2. What if the variable Income had a population mean of 39.5 (in 1000s of $) and a population standard deviation of 14.5 (in 1000s of $). A random sample of n=50 is taken.
a. What is the probability that our sample will have a sample mean greater than 41 (in 1000s)?
b. What is the probability that our sample will have a sample mean less than 38 (in 1000s)?
c. 95% of the time our sample will have a sample mean between what two values?
d. In Part a, you obtained the probability that a sample mean would be greater than 41. Does this probability lead you to doubt that the given population mean (39.5, in 1000s) is correct?
Yes or No, why/why not?
Next, using z procedures, run the following statistical tests to answer the following research questions. For each analysis, state the Null and Alternative hypotheses, state the result of your test, the test statistic, the p-value, and your business decision about the variable tested.
Is the population mean age of cardholders in this market significantly different than 40 years?
Is the population mean income of cardholders in this market significantly more than $125,000?
Is the population mean amount charged of cardholders in this market significantly different than $4000.
Is the population mean household size of cardholders in this market significantly greater than 3?
For all tests, use an alpha = .05. Also, regardless of significance results, include a 95% confidence interval for the population mean of each variable. For all tests, use z procedures for the population mean. You may use the sample standard deviation for each variable as an estimate of sigma. N = 77.
Grading
75% of full credit will be given if all charts, graphs, tables, and statistics are correctly produced and added to the report. The remaining will be earned only if the report is the correct format, correct and useful interpretation of the analyses is included, and meaningful results are presented in the results section.
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