In: Statistics and Probability
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?
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.