Question

. a 95% confidence interval for the mean of a population is to be constructed and must be accurate to within 0.3 unit. a preliminary sample standard deviation is 2.9. find the he smallest sample size n that provides the desired accuracy.

Answer 1

The smallest sample size for the 95% confidence interval for the mean of the population is 359 .

Given the standard deviation is 2.9 , hence  σ =2.9

Margin of error = E = 0.3

At 95% confidence level the z is ,

α = 1 - 95% = 1 - 0.95 = 0.05

α/2 = 0.05 / 2 = 0.025

Zα/2 = Z₀.₀₂₅ = 1.96

Now we know that the sample size is calculated using the formula:

$n = (z_{\frac{\alpha}{2}} \times \frac{\sigma}{E})^2$

n = [Z₀.₀₂₅ × σ / E] ²

n = ( 1.96×2.9  /0.3  )²

n = 358.976

n≈ 359

Sample size = n = 359

A confidence interval is a group of estimates for a parameter that is unknown (CI). Although occasionally other criteria, such as 90% or 99%, may also be used to generate confidence intervals. The average degree of confidence has increased to 95%.

The percentage of long-term associated CIs that contain the parameter's actual value is measured by the confidence level. For instance, the parameter's actual value should be present in 95% of all intervals generated at the 95% confidence level.

To learn more about confidence interval visit:

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