1) To aid in planning the development of a tourist shopping area, a state agency wants to estimate the average dollar amount spent by a tourist in an existing shopping area. A simple random sample of 56 tourists gave an average of $258 with standard deviation of $85.
a) Give a 95% confidence interval for the average of the population of all such tourists.
b) Repeat for sample size of 16, but same sample statistics. Also, the population is known to have a normal distribution.
c) What is a sampling unit (the noun and its modifiers that describe 1 item in the sample)?
d) What is the measurement for one item in the sample?
e) What is the population?
2) Before launching its Buyers' Assurance Program, American Express wanted to estimate the proportion of cardholders who would be interested in this automatic insurance coverage plan. A SRS of 250 American Express card accounts was selected and sent questionnaires. (Looks like they are assuming that all 250 responded, so the sample size is n = 250.) 121 responded expressing interest in the plan.
a) Give a 99% CI for the proportion of all American Express accounts that would be interested.
b) What is a sampling unit (the noun and its modifiers, describing 1 item in the sample)?
c) What is the measurement?
d) What is the population?
This solution is comprised of detailed explanation and step-by-step calculation of the given problems and provides students with a clear perspective of the underlying concepts.