Stat 301 – Quiz 24 Solutions

(b) We expect the samples to be skewed to the right like the populations. We do not expect them to be approximately normal, for any sample size, as confirmed by my graph below.

(c) We do expect the distribution of the difference in sample means to be approximately normal, as confirmed by my graph below.

(d) The CLT (really rules for random variables) predicts that the previous distribution will have a standard deviation of = 0.5597. This is reasonably close to my simulation results.

(e) The above distribution is centered at about -0.26. This is because = -0.228. So negative values correspond to females having more close friends on average. The above graph shows that -0.5 is very close to the center of the distribution and we would not be at all surprised to randomly obtain = 0.50. However, -1 is a little more borderline, a little more than 1 SD from the mean but less than 2 SD from the mean). So it would be a little surprising. We would be a little surprised by not super surprised to randomly obtain = 0.50.