6.119 Planning the dining court survey. 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. The hypotheses are

H₀: μ = 4

H_a: μ > 4

and they’ve decided they want adequate power to detect a mean of at least 4.25.

1. (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.

2. (b) Given α = 0.05, for what values of will you reject H₀?

3. (c) Using μ = 4.25, what is the probability that will fall in the region defined in part (b)?

4. (d) Will a sample size of n = 100 give you adequate power? Explain your answer.

5. (e) Use the Statistical Power applet or statistical software to determine the sample size n that gives you power near 0.80.