Use Table B for a simulation. We can construct a sampling distribution by hand in the case of a very small sample from a very small population.

The population contains 10 students. Here are their scores on an exam:

Student 0 1 2 3 4 5 6 7 8 9 Score 82 62 80 58 72 73 65 66 74 62 The parameter of interest is the mean score, which is 69.4. The sample is an SRS of n = 4 students drawn from this population. The students are labeled 0 to 9 so that a single random digit from Table B chooses one student for the sample.

(a) Use Table B to draw an SRS of size 4 from this population. Write the four scores in your sample and calculate the mean x of the sample scores. This statistic is an estimate of the population parameter.

(b) Repeat this process 9 more times. Make a histogram of the 10 values of x. You are constructing the sampling distribution of x. Is the center of your histogram close to 69.4? (Ten repetitions give only a crude approximation to the sampling distribution. If possible, pool your work with that of other students—using different parts of Table B—to obtain several hundred repetitions and make a histogram of the values of x. This histogram is a better approximation to the sampling distribution.)