Question

4. You want to estimate the mean amount spent by customers at a local gas station with 98%

confidence and a margin of error of no more than $2. Preliminary data suggests that s = $5.1 is a
reasonable estimate for the standard deviation for all customers. How large a sample do you need

Answer 1

To estimate the sample size, we can use the formula:

n = (z*sigma / E)^2

where:

z = z-score corresponding to the desired confidence level (in this case, 98% confidence level corresponds to a z-score of 2.33)

sigma = estimated standard deviation (given as $5.1)

E = maximum margin of error (given as $2)

Plugging in the values, we get:

n = (2.33*5.1 / 2)^2 = 68.89

Rounding up to the nearest whole number, we get a sample size of n = 69. Therefore, we need a sample size of at least 69 to estimate the mean amount spent by customers at the local gas station with 98% confidence and a margin of error of no more than $2.