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 (mu) 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 (mu). Assuming that the standard deviation of the population of shopping times at the supermarkets is 26 minutes, what is the minimum sample size she must collect in order for her to be 95% confident that her estimate is within 5 minutes of (mu) ?

Question

Atkinson

Mathematics

2 April, 10:05

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 (mu) 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 (mu). Assuming that the standard deviation of the population of shopping times at the supermarkets is 26 minutes, what is the minimum sample size she must collect in order for her to be 95% confident that her estimate is within 5 minutes of (mu) ?

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Jessie Campbell · Answer 1

The formula to calculate the sample size is:

n = Z number * standard deviation / confidence estimate) ^2

The z number for 95% confidence is 1.96

The standard deviation is given as 26 minutes.

The confidence estimate is given as 5 minutes.

The sample size is: (1.96 * 26/5) ^2 = 103.87 = 104 shoppers.