Question 1 - If the population from which the samples (Sample size is large) are drawn follows normal distribution with mean µ and standard deviation σ then the sample mean follows

Question 2 - Sample mean follows normal distribution with mean 49 and variance of 36. Assuming sample size to be 81, relation between standard error of mean (SEM) and margin of error (MOE) for 95% confidence level is

Standard error of mean = σ / SQRT(n)
Margin of error = Z * (σ / SQRT(n)) where Z depends on confidence level

Question 3 - Given margin of error as 3 and sample mean as 5, 95% confidence intervals for estimating population mean is given by

Question 4 - As sample size n increases, width of the confidence interval decreases given other parameters constant

Question 5 - Given other parameters constant, width of the confidence interval decreases as confidence level increases.