Question

A statistics practitioner took a random sample of 43 observations from a population whose standard deviation is 23 and computed the sample mean to be 95. Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits. A. Estimate the population mean with 95% confidence.

Answer 1

Confidence interval = (88.12, 101.88)

Explanation:

Confidence interval gives a range of values where the mean can be obtained with a certain level of confidence.

Confidence interval = (Sample mean) ± (Margin of error)

Sample mean = 95

Margin of Error = (critical value) × (standard deviation of the distribution of sample means)

Critical value = 1.960 (this is the z-score value, we will be using the z-distribution because the standard deviation given is for the population)

Standard deviation of the distribution of sample means = σ/√n

where σ = population standard deviation = 23

n = sample size = 43

Standard deviation of the distribution of sample means = (23/√43) = 3.51

Margin of error = 1.960 × 3.51 = 6.88

Confidence interval = (Sample mean) ± (Margin of error) = 95 ± 6.88

Confidence interval = (88.12, 101.88)

Hope this Helps!!!