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) 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.

b)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.