(1) The lifetime of a certain brand of battery is known to have a standard deviation of 19.8 hours. Suppose that a random sample of 50 such batteries has a mean lifetime of 40.9 hours. Based on this sample, find a 95% confidence interval for the true mean lifetime of all batteries of this brand. Then complete the table below.
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.
What is the lower limit of the 95% confidence interval?
What is the upper limit of the 95% confidence interval?
(2) Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The executives hire a statistical consultant and ask her to determine the mean shopping time, of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate mean. Assuming that the standard deviation of the population of shopping times at the supermarkets is 29 minutes, what is the minimum sample size she must collect in order for her to be 99% confident that her estimate is within 3 minutes of mean?
Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).
The solution provides step by step method for the calculation of confidence interval sample size for population mean. . Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.