Question 8 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
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% confidence interval for the true mean difference (company A – company B) in satisfaction ratings is –2.5 to 1.5. 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% confidence interval?
Answer
A
No, the confidence interval does not consist entirely of positive numbers.
B
No, the confidence interval does not consist entirely of negative numbers.
C
Yes, the confidence interval includes negative numbers as well as positive numbers.
D
Yes, the confidence interval includes more negative numbers than positive numbers.
Explanation
The interval is for company A’s mean rating minus company B’s mean rating. If customers were more satisfied with B, the true difference would be negative, so the confidence interval would need to consist entirely of negative numbers to support that claim. This interval runs from –2.5 to 1.5 and includes positive values, so it does not establish that B’s ratings are higher. The claim is not supported by the interval.
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