Question

Calculate the 95% confidence interval when n=54, σ=0.75, and μ=3

Answer 1

To calculate the 95% confidence interval, use the formula: Confidence Interval = sample mean ± margin of error. The margin of error can be calculated using the formula: Margin of Error = Z * (σ / √n), where Z is the z-score corresponding to the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96. Plug in the values and calculate the interval as (2.8256, 3.1744).

Step-by-step explanation:

To calculate the 95% confidence interval, we can use the formula:

Confidence Interval = sample mean ± margin of error

Given that n = 54, σ = 0.75, and μ = 3, we can calculate the margin of error using the formula:

Margin of Error = Z * (σ / √n)

Where Z is the z-score corresponding to the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.

Plugging in the values:

Margin of Error = 1.96 * (0.75 / √54) = 0.1744

Now we can calculate the confidence interval:

Confidence Interval = 3 ± 0.1744 = (2.8256, 3.1744)

Therefore, the 95% confidence interval when n = 54, σ = 0.75, and μ = 3 is (2.8256, 3.1744).