Estimating a Population Mean

Question 1

Estimator of population mean - 3

Answer 1

• The sampling distribution of the sampling mean, estimates the population mean.
• The estimator is unbiased, it targets the population mean.
• Standard deviation of the sampling distribution will tell us how good the estimator is.

Question 2

Confidence intervals Population Mean - 4

Answer 2

• Range of values used to estimate the true value of the mean. Based on a confidence level of 95% we are sure that 95% of the samples of size n will contain the sample mean
• By using approximate distribution, we can construct confidence intervals.
• If the standard deviation is not known we need to use the sample standard deviation.
• [bar x_n - E, bar x_n + E] is the confidence interval

Question 3

Margin of error - 3

Answer 3

• Denoted as E
• E = z score_(alpha/2) * (Sample sd / √n)
• For the error to be smaller than E_max we need a sample size of n ≥ ((z score * sd)/E_max)^2