Question

Use the sample information x¯ = 36, σ = 7, n = 16 to calculate the following confidence intervals for μ assuming the sample is from a normal population. (a) 99 percent confidence. (Round your answers to 4 decimal places.)

Answer 1

To calculate the confidence interval for μ, we can use the formula:

Confidence Interval = x¯ ± (Z * (σ/√n))

where:

x¯ = sample mean

σ = population standard deviation

n = sample size

Z = Z-score corresponding to the desired confidence level

For a 99 percent confidence level, the Z-score is 2.576.

Plugging in the given values:

Confidence Interval = 36 ± (2.576 * (7/√16))

Calculating the value inside the parentheses:

Confidence Interval = 36 ± (2.576 * (7/4))

Simplifying:

Confidence Interval = 36 ± (2.576 * 1.75)

Calculating the product:

Confidence Interval = 36 ± 4.514

Rounding the values to 4 decimal places:

Lower bound = 36 - 4.514 = 31.486

Upper bound = 36 + 4.514 = 40.514

Therefore, the 99 percent confidence interval for μ is (31.486, 40.514).