The article "Most Canadians Plan to Buy Treats, Many Will Buy Pumpkins, Decorations and/or Costumes" (Ipsos-Reid, October 24, 2005) summarized results from a survey of 1000 randomly selected Canadian residents. Each individual in the sample was asked how much he or she anticipated spending on Halloween during 2005. The resulting sample mean and standard deviation were $46.65 and $83.70, respectively.
a. Explain how it could be possible for the standard deviation of the anticipated Halloween expense to be larger than the mean anticipated expense.
b. Is it reasonable to think that the distribution of the variable anticipated Halloween expense is approximately normal? Explain why or why not.
c. Is it appropriate to use the t confidence interval to estimate the mean anticipated Halloween expense for Canadian residents? Explain why or why not.
d. If appropriate, construct and interpret a 99% confidence interval for the mean anticipated Halloween expense for Canadian residents.