The sample size is 96.
The range of values that we observe in our sample and for which we anticipate finding the value that accurately reflects the population is referred to as a confidence interval.
The margin of error is a statistic that describes how much random sampling error there is in survey results.
The confidence interval is,
C = 95% = 0.95
The margin of error is,
E = 10
The population standard deviation is,
σ = 40
The formula for sample size is:
n = ( ( Z × σ ) / E )²
Area = ( 1 + c )/2 = ( 1 + 0.95)/2 = 1.95 / 2 = 0.975
From the z table, the p-value is 1.96.
sample size n = ( ( 1.96 × 50 ) / 10 )²
n = ( 98 / 10 )²
n = ( 9.8 )²
n = 96.04
n ≈ 96
Therefore, the required sample size is 96.
Learn more about sample size here:
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