Final Answer:
a. The point estimate of the population mean is 10.125.
b. The point estimate of the population standard deviation is approximately 3.079.
c. With 95% confidence, the margin of error for the estimation of the population mean is 2.424.
d. The 95% confidence interval for the population mean is approximately (7.7, 12.5).
Step-by-step explanation:
a. To find the point estimate of the population mean, you sum up all the values given (10 + 8 + 12 + 16 + 13 + 11 + 6 + 4) and divide by the number of values (8). This results in a mean of 10.125.
b. To estimate the population standard deviation, you use the formula for the sample standard deviation. For this dataset, after calculating, the sample standard deviation is approximately 3.079.
c. To determine the margin of error for the estimation of the population mean with 95% confidence, you can use the formula: Margin of Error = Z * (σ / √n), where Z is the Z-score corresponding to the confidence level. For 95% confidence, Z ≈ 1.96. The standard deviation (σ) was estimated in part b, and n is the sample size (8). So, the margin of error is approximately 2.424.
d. The 95% confidence interval for the population mean is calculated by taking the point estimate ± margin of error. Using the point estimate from part a (10.125) and the margin of error from part c (2.424), the interval spans from approximately 7.7 to 12.5. This means we are 95% confident that the true population mean falls within this range.