Question

Construct the confidence interval for the population mean p.C=0.95, x = 4.2, σ = 0.4, and n = 59. A 95% confidence interval for p is:

a) (3.43, 4.97)

b) (3.52, 4.88)

c) (3.34, 5.06)

d) (3.29, 5.11)

Answer 1

Using the z-value for a 95% confidence level (approximately 1.96) and the provided statistics, the 95% confidence interval for the population mean is approximately (4.098, 4.302). The options provided in the question appear to contain a typo since none match these calculations.

Step-by-step explanation:

To construct the confidence interval for the population mean (p) with the given specifications (C=0.95, x = 4.2, σ = 0.4, and n = 59), we use the normal distribution because the population standard deviation (σ) is known. The 95% confidence interval is calculated by using the z-value that corresponds to a 95% confidence level, which is approximately 1.96 (from z-tables).

The formula to calculate the confidence interval is:

x ± (z * (σ/√n))

Plugging in the values, we have:

4.2 ± (1.96 * (0.4/√59))

Calculating the margin of error:

1.96 * (0.4/√59) ≈ 1.96 * (0.052) ≈ 0.102

Therefore, the 95% confidence interval is:

(4.2 - 0.102, 4.2 + 0.102) = (4.098, 4.302)

The answer provided looks like it might be a typo, since none of the listed options match our calculated interval. Hence, the correct interval is not listed.