Let the random variable X describe the dollar amount spent in supermarket impulse buying in 10-minute (unplanned) shopping interval. Based upon a Denver Post article, the mean of probability distribution of x is $20 and standard deviation is $7. Suggest a random sample of n = 100 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket.
A) Can the sampling distribution of the sample means, for the 100 shoppers, be assumed to have a normal distribution? Why?
What is the mean of the sampling distribution?
What is the standard deviation of the sampling distribution?
B) In answering part A), what assumptions did you make about the distribution of the variable?
1) No assumptions were made because the sample size is less than 25.
2) It was assumed that the random variable x was normally distributed.
3) No Assumptions were made because the sample size is greater than 25.
4) No assumptions were made because the sampling distribution is normal, regardless of the distribution of the variable under consideration.