Time-of-day pricing for electricity. Time-of-day pricing is a plan by which customers are charged a lower rate for using electricity during off-peak (less demanded) hours. One experiment (reported in the Journal of Consumer Research, June 1982) was conducted to measure customer satisfaction with several time-of-day pricing schemes. The experiment consisted of two factors, price ratio (the ratio of peak to off-peak prices) and peak period length, each at three levels. The 3 × 3 = 9 combinations of price ratio and peak period length represent the nine time-of-day pricing schemes.
For each pricing scheme, customers were randomly selected and asked to rate satisfaction with the plan using an index from 10 to 38, with 38 indicating extreme satisfaction. Suppose four customers were sampled for each pricing scheme. The table on p. 706 gives the satisfaction scores for these customers. [Note: The data are based on mean scores provided in the Journal of Consumer Research article.]
(a) Use a statistical software package to conduct an analysis of variance of the data. Report the results in an ANOVA table.
(b) Compute the nine customer satisfaction index means.
(c) Plot the nine means from part b on a graph similar to Figure. Does it appear that the two factors, price ratio and peak period length, interact? Explain.
(d) Do the data provide sufficient evidence of interaction between price ratio and peak period length? Test using α = .05.
(e) Do the data provide sufficient evidence that mean customer satisfaction differs for the three peak period lengths? Test using α = .05.
(f) When is the test of part e appropriate?
(g) Find a 90% confidence interval for the mean customer satisfaction rating of a pricing scheme with a peak period length of 9 hours and pricing ratio of 2:1.
(h) Find a 95% confidence interval for the difference between the mean customer satisfaction ratings of pricing schemes 9 hours, 8:1 ratio and 6 hours, 8:1 ratio. Interpret the interval.
(i) Use Tukey's multiple comparisons procedure to compare the mean satisfaction scores for the three peak period lengths under each of the three pricing ratios. Identify the means that appear to differ under each pricing ratio. Use α = .01.