Directions You will compute a 90% and 95% confidence interval for three problems. Use the flow chart in the Bluman Elementary Statistics text (Chapter 7) to determine the proper form of confidence interval statistic for each problem (Z-σ, Z-s, or t-s) Your corporation owns a hotel chain with several hundred hotel locations around the US and Canada. Locations typically are in metro areas serving both business and leisure customers. Within the last few years your corporation entered into a number of franchisee agreements, allowing independent operators to use the chain’s trademarks, signage, award points program, and corporate web and call center services. Your firm used the same advertising strategy, trademark set, signage, and points program for years, and Management feels it’s time for a refresh. A business analysis team is experimenting with advertising and other marketing changes in a few test markets, and you serve as their statistical consultant. You will compute confidence intervals for the team as they provide test market study data to you. Your corporate locations have been in place a long time, and you suspect the new signage and advertising might have a stronger impact on corporate versus franchised locations. You decide to separate the data set, and compute confidence intervals separately for the 25 corporate locations in the data set. The corporate locations have an average revenue of $430,000 during the test period, with a standard deviation of just $36,000. Nonetheless the business analysis team remains comfortable using the standard deviation from previous studies. a) State the proper confidence interval formula. b) Compute the 90% and 95% confidence intervals for test market average revenue. c) For each confidence interval, answer the question: “Does the test market confidence interval contain the average revenue of the chain’s typical hotels ($400,000 per month). d) Note which is larger, the 90% or the 95% confidence interval. Why?
Directions You will compute a 90% and 95% confidence interval for three problems. Use the flow chart in the Bluman Elementary Statistics text (Chapter 7) to determine the proper form of confidence interval statistic for each problem (Z-σ, Z-s, or t-s)
Your corporation owns a hotel chain with several hundred hotel locations around the US and Canada. Locations typically are in metro areas serving both business and leisure customers. Within the last few years your corporation entered into a number of franchisee agreements, allowing independent operators to use the chain’s trademarks, signage, award points program, and corporate web and call center services. Your firm used the same advertising strategy, trademark set, signage, and points program for years, and Management feels it’s time for a refresh. A business analysis team is experimenting with advertising and other marketing changes in a few test markets, and you serve as their statistical consultant. You will compute confidence intervals for the team as they provide test market study data to you.
Your corporate locations have been in place a long time, and you suspect the new signage and advertising might have a stronger impact on corporate versus franchised locations. You decide to separate the data set, and compute confidence intervals separately for the 25 corporate locations in the data set. The corporate locations have an average revenue of $430,000 during the test period, with a standard deviation of just $36,000. Nonetheless the business analysis team remains comfortable using the standard deviation from previous studies. a) State the proper confidence interval formula. b) Compute the 90% and 95% confidence intervals for test market average revenue. c) For each confidence interval, answer the question: “Does the test market confidence interval contain the average revenue of the chain’s typical hotels ($400,000 per month). d) Note which is larger, the 90% or the 95% confidence interval. Why?
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