Gproblem 2i given n i. i.d. random variables x1, x2, . . , xn, each with mean µ and variance σ 2 > 0 (both unknown parameters), we saw in class that the sample mean x = 1 n pn i=1 xi is an unbiased estimator of the mean µ, whereas the so-called sample variance s 2 = 1 n − 1 xn i=1 xi − x ? 2 is an unbiased estimator of the variance σ 2 . in other words, e(s 2 ) = σ 2 . is s = √ s 2 an unbiased estimator of the standard deviation σ? if not, does s tend to underestimate or overestimate the standard deviation? hint: very little computation is needed. start by writing the formula for computing the variance of s

Ascientist studied a population of workers to determine whether verbal praise and/or tangible rewards affect employee productivity. in the study, some workers were offered verbal praise, some were offered tangible rewards (gift cards, presents, and some were offered neither. the productivity of each participant was measured throughout the study by recording the number of daily tasks completed by each employee. which inference might the scientists make based on the given information? a.) the number of daily tasks completed by each employee may influence the dependent variable, which is whether the employee receives verbal praise, tangible rewards, or neither. b.) verbal praise and/or tangible rewards may influence the independent variable, which is the number of daily tasks completed by each employee. c.) verbal praise and/or tangible rewards may influence the dependent variable, which is the number of daily tasks completed by each employee. d.) the dependent variables, which are verbal praise and tangible rewards, may influence the number of daily tasks completed by each employee.