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Question
NARRBEGIN: SA_91_94Q-Mart is interested in comparing customer who used 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 card. 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.
| Summary statistics for two samples | ||
| Female | Male | |
| Sample sizes | 25 | 22 |
| Sample means | 102.23 | 86.46 |
| Sample standard deviations | 93.393 | 59.695 |
| Confidence interval for difference between means | ||
| Sample mean difference | 15.77 | |
| Pooled standard deviation | 79.466 | |
| Std error of difference | 23.23 | |
(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.
Answer
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