Many credit card companies offer incentives, such as cash back and airline miles

Question

Many credit card companies offer incentives, such as cash back and airline miles, to encourage customers to use the card frequently. A credit card company is interested in determining whether a new incentive could increase average customer spending. To determine this, the company took two random samples of 500 cardholders from its database (so 500 + 500 = 1000 customers in total). The company will calculate a confidence interval to determine if the difference in mean spending between the group with an incentive (Group 1: "Incentive") and the group without that incentive (Group 2: "No incentive") is significant. A 95% confidence interval for the difference in means between the two groups was found to be $46.79 to $193.06. Which of the following gives the correct interpretation of the interval? Read carefully!

The company can be 95% confident, based on the method used to calculate the interval, that 95% of customers with an incentive would increase their spending by between $46.79 and $193.06 on average. Because the interval does not contain the value of 0, the company can conclude that the incentive, on average, will increase spending.

The company can be 95% confident, based on the method used to calculate the interval, that the true difference in mean spending between customers offered an incentive and those not offered an incentive is between $46.79 and $193.06. Because the interval does not include the value of 0, the company can conclude that the incentive, on average, will increase customer spending.

The company can be 95% confident, based on the method used to calculate the interval, that the true difference in mean spending between customers offered an incentive and those not offered an incentive is between $46.79 and $193.06. Because the interval contains the value of 100, the company cannot conclude that the incentive, on average, will increase spending.

The company can be 95% confident, based on the method used to calculate the interval, that the difference in total spending between customers offered an incentive and those not offered an incentive is between $46.79 and $193.06. Because the interval does not contain the value of 0, the company can conclude that the incentive will increase each customer's spending.

The company can be 95% confident, based on the method used to calculate the interval, that there is a 95% chance that the difference in mean spending between customers offered an incentive and those not offered an incentive is between $46.79 and $193.06. Because the interval does not contain the value of 0, the company can conclude that the incentive, on average, will increase spending.

The company can be 95% confident, based on the method used to calculate the interval, that 95% of customers with an incentive would increase their spending by between $46.79 and $193.06 on average. Because the interval does not contain the value of 0, the company can conclude that the incentive, on average, will increase spending.

The company can be 95% confident, based on the method used to calculate the interval, that the true difference in mean spending between customers offered an incentive and those not offered an incentive is between $46.79 and $193.06. Because the interval does not include the value of 0, the company can conclude that the incentive, on average, will increase customer spending.

The company can be 95% confident, based on the method used to calculate the interval, that the true difference in mean spending between customers offered an incentive and those not offered an incentive is between $46.79 and $193.06. Because the interval contains the value of 100, the company cannot conclude that the incentive, on average, will increase spending.

The company can be 95% confident, based on the method used to calculate the interval, that the difference in total spending between customers offered an incentive and those not offered an incentive is between $46.79 and $193.06. Because the interval does not contain the value of 0, the company can conclude that the incentive will increase each customer's spending.

The company can be 95% confident, based on the method used to calculate the interval, that there is a 95% chance that the difference in mean spending between customers offered an incentive and those not offered an incentive is between $46.79 and $193.06. Because the interval does not contain the value of 0, the company can conclude that the incentive, on average, will increase spending.

Explanation / Answer

The difference in sample means is used to estimate the difference in population means. The accuracy of the estimate is revealed by a confidence interval.

Further, If the confidence interval for the difference does not contain zero, we can conclude that there is a statistically significant difference in the two population values at the given level of confidence.

So answer is

The company can be 95% confident, based on the method used to calculate the interval, that the true difference in mean spending between customers offered an incentive and those not offered an incentive is between $46.79 and $193.06. Because the interval does not include the value of 0, the company can conclude that the incentive, on average, will increase customer spending.

The company can be 95% confident, based on the method used to calculate the interval, that the true difference in mean spending between customers offered an incentive and those not offered an incentive is between $46.79 and $193.06. Because the interval does not include the value of 0, the company can conclude that the incentive, on average, will increase customer spending.

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.