Question

Assume that a sample is used to estimate a population mean μ. Find the 80% confidence interval for a sample of size 57 with a mean of 21.8 and a standard deviation of 8.8 .

80% C.I. =

Answer 1

To find the 80% confidence interval for a sample of size 57 with a mean of 21.8 and a standard deviation of 8.8, use the formula: x ± Z * (σ/√n). Plugging in the values, the 80% confidence interval is (20.4, 23.2).

Step-by-step explanation:

To find the 80% confidence interval for a sample of size 57 with a mean of 21.8 and a standard deviation of 8.8, we can use the formula: x ± Z * (σ/√n), where x is the sample mean, Z is the Z-value corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

Since we want an 80% confidence interval, the Z-value we need to use is 1.28 (corresponding to 80% in the standard normal table). Plugging in the values, we get:

Lower limit = 21.8 - 1.28 * (8.8/√57) = 20.4

Upper limit = 21.8 + 1.28 * (8.8/√57) = 23.2

Therefore, the 80% confidence interval is (20.4, 23.2).