Question

a random sample of 25 students in an introductory statistics course at a particular university were asked how many hours of sleep they got last night. a 95% confidence interval for the mean number of hours of sleep all introductory statistics students at this university got last night was (4.6,6.2). the researcher compared this confidence interval to a 95% confidence interval for the mean number of hours of sleep all other students at this university not taking introductory statistics got last night, which was (6.7,7.5). which of the following statements is true?

choose the correct answer below.

a. because the confidence intervals do not overlap, it appears that non - introductory statistics students at this university got more sleep last night, on average, than introductory statistics students at this university.

b. because the confidence intervals do not overlap, it appears that all non - introductory statistics students at this university got more sleep last night than all of the introductory statistics students at this university.

c. because the confidence intervals do not overlap, a comparison between the means of two groups cannot be made.

d. because the confidence intervals do not overlap, it does not appear that non - introductory statistics students at this university got more sleep last night, on average, than introductory statistics students at this university.

Explanation:

• Confidence intervals give an estimate of the range within which the population mean is likely to lie.
• When two confidence intervals (for the means of two different groups) do not overlap, it suggests a significant difference in the means.
• Here, the confidence interval for non - Introductory Statistics students \((6.7,7.5)\) is entirely above the confidence interval for Introductory Statistics students \((4.6,6.2)\). This implies that, on average, non - Introductory Statistics students got more sleep.
• Option B is wrong because confidence intervals are about means (average values), not about individual values. We cannot say all non - Introductory Statistics students got more sleep than all Introductory Statistics students.
• Option C is wrong because non - overlapping confidence intervals do allow for a comparison of means.
• Option D is wrong as the non - overlapping (with the non - Introductory interval above the Introductory interval) does suggest that non - Introductory students got more sleep on average.

Answer:

A. Because the confidence intervals do not overlap, it appears that non - Introductory Statistics students at this university got more sleep last night, on average, than Introductory Statistics students at this university.