Final answer:
a. The point estimate for the population mean is the sample mean. b. To calculate the error bound at a 95% confidence level, use the critical value. c. The confidence interval is calculated by adding and subtracting the error bound from the sample mean.
Step-by-step explanation:
a. The point estimate for the population mean is the sample mean. In this case, the sample mean is and the sample standard deviation is .
b. To calculate the error bound at a 95% confidence level, we need to find the critical value corresponding to 2.5% in each tail of the distribution. Using a standard normal distribution table or calculator, the critical value is approximately 1.96. The error bound is then calculated as: Error bound = Critical value x Standard deviation / Square root of sample size = 1.96 x / square root of .
c. The confidence interval is calculated by subtracting the error bound from the sample mean to get the lower bound, and adding the error bound to the sample mean to get the upper bound. Confidence interval = (lower bound, upper bound) = (sample mean - error bound, sample mean + error bound) = ( - , + ).
d. The confidence interval provides a range of values within which we can be 95% confident that the true population mean falls. It means that if we were to take multiple random samples and calculate their confidence intervals, approximately 95% of those intervals would contain the true population mean.