Calculate the confidence interval interval

Solved Step by Step With Explanation- Confidence Intervals for Mean

Questions

b. Provide a 95% confidence interval for the population mean.

c. Provide a 99% confidence interval for the population mean.

Confidence Interval = X̄ ± Z * (σ / √n)

Where:

a. For a 90% confidence interval:

Confidence level = 90%, so α (alpha) = 1 - 0.90 = 0.10.

b. For a 95% confidence interval:

Confidence level = 95%, so α = 1 - 0.95 = 0.05.

Confidence level = 99%, so α = 1 - 0.99 = 0.01.

We want a 99% confidence interval, so the critical value Z for a two-tailed test is Z(0.01/2) = Z(0.005), which is approximately 2.576.

Confidence Interval (90%) ≈ 35 ± 1.645 * (7 / √70)

b. 95% confidence interval: