Q-Mart Is Interested in Comparing Customers Who Use Its Own

question 75

Essay

Q-Mart is interested in comparing customers who use its own charge card with those who use other types of credit cards. Q-Mart would like to know if customers who use the Q-Mart card spend more money per visit, on average, than customers who use some other type of credit cards. They have collected information on a random sample of 38 charge customers as shown below. On average, the person using a Q-Mart card spends $192.81 per visit and customers using another type of card spend $104.47 per visit.
-(A) Using a t - value of 2.0281, calculate a 95% confidence interval for the difference between the average Q-Mart charge and the average charge on another type of credit card.
(B) What are the degrees of freedom for the t - multiple in this calculation? Explain how you would calculate the degrees of freedom in this case.
(C) What is the assumption in this case that allows you to use the pooled standard deviation for this confidence interval?
(D) Would you conclude that there is a significant difference between the two types of customers in this case? Explain.

---

Definitions:

Probability

The quantification of an event's probability, expressed as a value from 0 to 1, where 0 means the event cannot happen and 1 means it will definitely occur.

Type I Error

The error made by rejecting a true null hypothesis, often referred to as a "false positive."

Type II Error

The error that occurs when a false null hypothesis is not rejected, also known as a "false negative."

Reducing

The process of decreasing or minimizing a quantity, dimension, or frequency.