Question

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
Ha: μ > 4
and 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?

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

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

*For reference:

6.38 Dining court survey. The dining court closest to your university residence has been
redesigned. A survey is planned to assess whether or not students think that the new design is an
improvement. It will contain eight questions; a seven-point scale will be used for the answers,
with scores less than 4 favoring the previous design and scores greater than 4 favoring the new
design (to varying degrees). The average of these eight questions will be used as the student’s
response. State the null and alternative hypotheses you would use for examining whether or not
the new design is viewed more favorably.

Answer 1