1. Suppose that 400 randomly selected OSU alumni were asked to rate the ...

  

1. Suppose that 400 randomly selected OSU alumni were asked to rate the university’s counseling services on a 1 to 10 scale. The sample mean (x¯) was found to be 8.6. Assume that the population standard deviation is known to be σ = 2.0.

(a) Alice computes the 95% confidence interval for the mean satisfaction score as 8.6 ± 1.96(2.0). What is her mistake? 

(b) After correcting her mistake in part (a), she states “I am 95% confident that the sample mean falls between 8.404 and 8.796.” What is wrong with this statement? 

(c) After quickly realizing her mistake in part (b), she states “95% of alumni ratings would fall between 8.404 and 8.796.” What is wrong with this statement?

(d) She realizes her mistake in part (c) and instead states “The probability that the true mean is between 8.404 and 8.796 is 0.95.” What misinterpretation is she making now?

(e) Finally, in her defense for using the Normal distribution to determine the confidence coefficient, she says “Because the sample size is quite large, the population of alumni ratings will be approximately normal.” Explain to Alice her misunderstanding and correct this statement.