Suppose a population consists of the 10 measurements (2, 3, 6, 8, 9, 12, 25, 29, 39, 50). Generate the 45 possible values for the sample mean based on a sample of n = 2 observations per sample.
a. Use the 45 sample means to determine whether the sampling distribution of the sample mean is approximately normally distributed by constructing a boxplot, relative frequency histogram, and normal quantile plot of the 45 sample means.
b. Compute the correlation coefficient and p-value to assess whether the 45 means appear to be sampled from a normal distribution.
c. Do the results in part (b) confirm your conclusion from part (a)?