A random sample of 100 customers is selected, and the mean difference in their satisfaction rating for company A and company B is calculated. A rating of 1 indicates that a customer is highly dissatisfied, and a rating of 5 indicates that a customer is highly satisfied. A 90 percent confidence interval for the true mean difference (company A – company B) in satisfaction ratings is negative 2 point 5 to 1 point 5 Based on the confidence interval, the owner of company B claims that customers are more satisfied with his company than with company A. Is this claim supported by the 90 percent confidence interval?
Answer
A
Yes, the confidence interval includes more negative numbers than positive numbers.
B
Yes, the confidence interval includes negative numbers as well as positive numbers.
C
No, the confidence interval does not consist entirely of negative numbers.
D
No, the confidence interval does not consist entirely of positive numbers.
Explanation
The confidence interval is for company A’s mean rating minus company B’s mean rating. For the owner’s claim that B has higher satisfaction to be supported by this interval, the difference would need to be entirely negative. Since the interval runs from −2.5 to 1.5 and includes positive values, it does not consist entirely of negative numbers; the claim is not supported.
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