Question

A sample of size 101 is taken from a normal population with a sample standard deviation s = 40.00. The lower and upper 0.025 points of the χ² distribution with 100 degrees of freedom are χ²(100,0.975) = 74.222 and χ²(100,0.025) = 129.561. What is the confidence interval for the population mean?

1) (74.222, 129.561)
2) (0, 129.561)
3) (74.222, [infinity])
4) (0, [infinity])

Answer 1

The confidence interval for the population mean can be calculated using the formula: Confidence Interval = Sample Mean ± (Critical Value) × (Standard Deviation / √(Sample Size)). In this case, the sample mean is unknown, but we can estimate it using the formula: Estimated Sample Mean = Sample Mean ± (Critical Value) × (Sample Standard Deviation / √(Sample Size)). The confidence interval for the population mean is approximately (68.957, 71.043).

Step-by-step explanation:

The confidence interval for the population mean can be calculated using the formula:

Confidence Interval = Sample Mean ± (Critical Value) × (Standard Deviation / √(Sample Size))

In this case, the sample mean is unknown, but we can estimate it using the formula:

Estimated Sample Mean = Sample Mean ± (Critical Value) × (Sample Standard Deviation / √(Sample Size))

Substituting the given values, we get:

Estimated Sample Mean = Sample Mean ± (1.96) × (40 / √101)

Simplifying the expression, the confidence interval for the population mean is approximately (68.957, 71.043).