Exercise 6.38 (page 364) describes a survey to assess whether a newly designed dining court is viewed more favorably than the old design. The organizers are considering randomly surveying n = 100 student patrons but would like some statistical advice. they've decided they want adequate power to detect a mean of at least 4.25.

a) The organizers have no idea of σ. You suggest a small pilot study, which gives s = 1.73. Based on this result, you decide to use σ = 2. Provide an explanation for this choice to the organizers.
b) Given α = 0.05, for what values of ¯x will you reject H₀?