Question

online courses: a sample of 261 students who were taking online courses were asked to describe their overall impression of online learning on a scale of 1-7, with 7 representing the most favorable impression. the average score was 5.45, and the standard deviation was 0.90. use the ti-84 plus calculator as needed.
(a) construct a 99.5% confidence interval for the mean score. round the answers to at least two decimal places.
a 99.5% confidence interval for the mean score is 5.29 < μ < 5.61.
(b) assume that the mean score for students taking traditional courses is 5.53. a college that offers online courses claims that the mean scores for online courses and traditional courses are the same. does the confidence interval contradict this belief?
the confidence interval select contradict this belief.
(options: does, does not)

Explanation:

Step1: Analyze the confidence interval

The confidence interval for the mean score of online courses is \(5.29<\mu <5.61\).

Step2: Check the claim

The claim is that the mean score for traditional courses is \(5.53\). Since \(5.53\) lies within the interval \(5.29 <\mu<5.61\) (because \(5.29<5.53<5.61\)), it means that the value \(5.53\) is a plausible value for the population mean \(\mu\) (assuming online and traditional courses have the same mean in this context of the problem's assumption).

Answer:

The confidence interval does not contradict the claim. Because \(5.53\) is within the interval \(5.29 <\mu<5.61\).