a. A statistics practitioner randomly sampled 100 observations from a population with a standard deviation of 5 and found that x is 10. Estimate the population mean with 90% confidence.

Question

a. A statistics practitioner randomly sampled 100 observations from a population with a standard deviation of 5 and found that x is 10. Estimate the population mean with 90% confidence.

Answer 1

Formula:

CI90 = mean + or - 1.645(sd/√n)

sd = standard deviation
n = sample size

Substitute the values from your problem into the formula and calculate.

Answer 2

To estimate the population mean with 90% confidence, you can use a confidence interval. The formula for the confidence interval is:

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

Where:
- x is the sample mean (10 in this case)
- Z is the Z-score corresponding to the desired confidence level (90% confidence corresponds to a Z-score of 1.645)
- σ is the standard deviation of the population (5 in this case)
- n is the sample size (100 in this case)

Now, let's plug in the values to calculate the confidence interval:

Confidence Interval = 10 ± (1.645 * (5/√100))

Confidence Interval = 10 ± (1.645 * 0.5)

Confidence Interval = 10 ± 0.8225

Therefore, the confidence interval estimate for the population mean with 90% confidence is 9.1775 to 10.8225. This means that we are 90% confident that the true population mean falls within this range.