Question

Determine the margin of error for an 80% confidence interval to estimate the population mean with σ=51 for the following sample sizes a) n=33 b) n=45 c) n=67

Answer 1

The margin of error for an 80% confidence interval can be calculated using the formula ME = Z * (σ / √n), where ME is the margin of error, Z is the Z-score, σ is the population standard deviation, and n is the sample size. For the given sample sizes of 33, 45, and 67, the margin of error is approximately 9.38, 7.82, and 5.84, respectively.

Step-by-step explanation:

To determine the margin of error for a confidence interval, we can use the formula:

ME = Z * (σ / √n)

where:

• ME is the margin of error
• Z is the Z-score associated with the confidence level
• σ is the population standard deviation
• n is the sample size

For an 80% confidence interval, the Z-score is 1.28.

a) For n = 33, ME = 1.28 * (51 / √33) ≈ 9.38

b) For n = 45, ME = 1.28 * (51 / √45) ≈ 7.82

c) For n = 67, ME = 1.28 * (51 / √67) ≈ 5.84