Question

A random sample of 52 observations was taken. The average in the sample was 80 with a variance of 400. Construct a 98% confidence interval for μ.

Answer 1

To construct a 98% confidence interval for the population mean (μ), calculate the standard error, find the Z value, and plug in the values to get the confidence interval range.

Step-by-step explanation:

To construct a 98% confidence interval for the population mean (μ), we can use the formula:

μ ± (Z)(σ/√n)

1. Calculate the standard error (σ/√n) where σ is the population standard deviation and n is the sample size. In this case, the standard error would be √(400/52).
2. Find the Z value corresponding to a 98% confidence interval. For a 98% confidence level, the Z value is approximately 2.33.
3. Plug in the values: μ ± (2.33)(√(400/52)).
4. Simplify to get the confidence interval range.

Therefore, we can construct a 98% confidence interval for μ using the given sample as (80 - 2.33(√(400/52)), 80 + 2.33(√(400/52))).