Question

The manager of a home improvement store wishes to estimate the mean amount of money spent in the store. The estimate is to be within $4.00 with a 95% level of confidence. The manager does not know the standard deviation of the amounts spent. However, he does estimate that the range is from $5.00 up to $155.00. How large of a sample is needed?

Answer 1

The manager of home improvement store wishes to estimate the mean amount of money spent in the store.

 

Given estimate is to be within $ 4. So E = 4

Upper and lower limits are 155 and 5 respectively.

Confidence level = 95%.

 

From the table showing area under normal curve, the value corresponding to 95% confidence is z = 1.96.

σ(Standard deviation) = range/6

                                    σ = 155 – 5/6

                                   σ = 150/6

                                   σ = 25

 

Therefore required sample size

n = (2σ/e)2

   = (1.96 × 25/4)2

   = (12.25)2

   = 150.06

 

Approximately the sample size is 150.

Approximately the sample size is 150.