Sampling invoices. We will illustrate the idea of a sampling distribution in the case of a very small sample from a very small population. The population contains 10 past-due invoices.

Here are the number of days each invoice is past due:

Invoice: 0 1 2 3 4 5 6 7 8 9 Days past due: 8 12 10 5 7 3 15 9 7 6 The parameter of interest is the mean of this population, which is 8.2 days. The sample is an SRS of n = 4 invoices drawn from the population. Because the invoices are labeled 0 to 9, a single random digit from Table B chooses one invoice for the sample.

(a) Use Table B to draw an SRS of size 4 from this population.

Write the past-due values for the days in your sample and calculate their mean x. This statistic is an estimate of the population parameter.

(b) Repeat this process 10 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 8.2? (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 at least 100 repetitions. A histogram of these values of x is a better approximation to the sampling distribution.)

APPLET