Namaste Yoga is considering keeping the virtual studio developed during the pandameic a permanaent feature for their community. The Marketing Manager has hired a consultant to design a survey to determine attitudes towards the service. In addition the percentage of young adults in Quebec practicing yoga and the average frequency per week are to be determined. The Marketing Manager wants to be 95% confident of the results and does not want the error to exceed 3 percentage points for yoga practioners ownership and 2 hours per week for average practice. Previous reports are not available for the percentage of youth yoga practioners, but some earlier studies do indicate that the average weekly practice is 6 hours with a variance of 4 hours.

a. What sample size would you recommend assuming that only the percentage of households with youth yogis is to be determined? Show all your calculations (5 points)

b. What sample size would you recommend assuming that only the average practice hours per week is to be determined? Show all your calculations. (5 points)

c. Due to budget constraints, Namaste decided to use a sample size of 582, and to maintain the confidence level at 95%. What is the consequence of doing so for the specified Namaste ownership error rate and for the average usage rate error rate? Show all your calculations. (5 points)

d. The actual results of the survey showed that 30% of young adults practice yoga and that the average practice 5 hours (variance=3). Compute the 95% confidence interval for the usage rate per week. (5 points)

e. The consultant who carried out the survey using systematic sampling found that some interviewers had skipped respondents who were hard to understand on the phone, and that some survey questions may not have been clear. She makes the following statement in her presentation to the management of the firm: "Based on the results, I can say with 95% confidence that the average young adult in Quebec who practices yoga, does so 5 hours a week. There is only a 5% probability that any mistakes that might have occurred in the survey process can affect the results". Discuss whether the consultant is justified in making the statement she did (in quotation marks). (5 points)