A sample of 263 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 5.53, and the standard deviation was 0.92.

a. Construct a 95% confidence interval for the mean score.

b. Assume that the mean score for students taking traditional courses is 5.55. 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 claim? Explain.