Given Information:
Confidence level = 95%
Error = 0.07
Mean = μ = 8.1
Standard deviation = σ = 2
Required Information:
Sample size = n = ?
Answer:
Sample size = n ≤ 2209
Step-by-step explanation:
The sample size required to create the specified confidence interval is given by
error ≤ z*(σ/√n)
Where z is the corresponding z-score of 95 percentile, n is the sample size and σ is the standard deviation and error is no more than 0.07
√n ≤ z*σ/error
n ≤ (z*σ/error)²
The z-score for 95% confidence level is 1.645
n ≤ (1.645*2/0.07)²
n ≤ 2209
Therefore, a sample size of n ≤ 2209 is required to create a 95% confidence interval with an error of no more than 0.07.