Question

Construcl an 80% confidence interval to estimate the population mean when

x =129 and s=28 for the sample sizes below a) n=30 b) n=60 c) n=80

Answer 1

To construct a confidence interval, use the formula CI = x ± (Z * (s/√n)). For each sample size, calculate the confidence interval using the given values of x = 129, s = 28, and Z for 80% confidence level.

Step-by-step explanation:

To construct a confidence interval, we use the formula:

CI = x ± (Z * (s/√n))

where:

• CI is the confidence interval
• x is the sample mean
• Z is the z-score corresponding to the desired confidence level
• s is the sample standard deviation
• n is the sample size

For each part of the question:

a) n = 30

Z = 1.28 (corresponding z-score for 80% confidence)

CI = 129 ± (1.28 * (28/√30))

CI = (117.95, 140.05)

b) n = 60

Z = 1.28

CI = 129 ± (1.28 * (28/√60))

CI = (123.03, 134.97)

c) n = 80

Z = 1.28

CI = 129 ± (1.28 * (28/√80))

CI = (122.16, 135.84)