Which statement is most nearly correct, other things being equal? a) doubling the sample size will cut the standard error of the mean in half. b) the standard error of the mean depends on the population size. c) quadrupling the sample size roughly halves the standard error of the mean. d) the standard error of the mean depends on the confidence level.2) the central limit theorem (clt) implies that: a) the population will be approximately normal if n ? 30.b) repeated samples must be taken to obtain normality. c) the distribution of the mean is approximately normal for large n. d) the mean follows the same distribution as the population.3)the owner of limp pines resort wanted to know the average age of its clients. a random sample of 25 tourists is taken. it shows a mean age of 46 years with a standard deviation of 5 years. the width of a 98 percent ci for the true mean client age is approximately: