Refer to Exercise 2.158 and the Journal of Statistics Education data on diamonds saved in the accompanying file. Consider the quantitative variable, number of carats, recorded for each of the 308 diamonds for sale on the open market.
a. Select a random sample of 30 diamonds from the 308 diamonds.
b. Find the mean and standard deviation of the number of carats per diamond for the sample.
c. Use the sample information, part b, to construct a 95% confidence interval for the mean number of carats in the population of 308 diamonds.
d. Interpret the phrase 95% confidence when applied to the interval, part c.
e. Refer to the mean of all 308 diamonds you calculated in Exercise 2.157. Does the "population" mean fall within the confidence interval of part c?