Given Information:
standard deviation = σ = 15 ft²
Confidence interval = 95%
Margin of error = 2.5 ft²
Required Information:
Sample size = n = ?
Answer:
Sample size = n ≈ 139
Step-by-step explanation:
The required number of observations can be found using
,
Me = z(σ/√n)
Where Me is the margin of error, z is the corresponding z-score of 95% confidence interval, σ is the standard deviation and n is the required sample size.
Rearrange the above equation to find the required number of sample size
√n = σz/Me
n = (σz/Me)²
For 95% confidence level, z-score = 1.96
n = (15*1.96/2.5)²
n = 138.29
since the sample size can't be in fraction so,
n ≈ 139
Therefore, a sample size of 139 would be needed.
