Two questions that I'm unsure of are below:

1). The variability of a statistic is described by:

a) the spread of its sampling distribution.

b) the amount of bias present

c) the vagueness in the wording of the question used to collect the sample data

d) the stability of the population it describes

(I chose letter "d"--but I'm not sure if this is correct.)

2) The law of large numbers states that as the number of observations drawn at random from a population with finite mean μ increases, the mean x̄ of the observed values:

a) gets larger and larger

b) gets smaller and smaller

c) tends to get closer and closer to the population mean μ

d) fluctuates steadily between one standard deviation above and one standard deviation below the mean

(I chose choice "c"--but again, am unsure of my answer)

1. A, variability is expressed in terms of range, standard deviation or variance.

2. C is correct.

To determine the correct answer to these questions, let's discuss the concepts involved.

1) The variability of a statistic refers to the degree to which different samples of the same size from the same population yield different values of that statistic. In this context, the variability is described by the spread of its sampling distribution. The sampling distribution represents the distribution of all possible sample statistics that could be obtained from repeated sampling of the same size from the population.

Option (a) mentions the spread of the sampling distribution, which accurately describes the variability of a statistic. Therefore, the correct answer is (a).

2) The law of large numbers relates to the behavior of the sample mean as the sample size increases. It states that the mean of a large number of independent and identically distributed observations will tend to approach the population mean.

Option (c) states that the mean of the observed values tends to get closer and closer to the population mean, which aligns with the law of large numbers. Therefore, the correct answer is (c).

So, your chosen answers of (d) for the first question and (c) for the second question are incorrect. The correct answers are (a) and (c), respectively.