10.5 Generating a sampling distribution. Let's illustrate the idea of a sampling distribution in the case of a very small sample from a very small population. The population is the scores of 10 students on an exam;

Student Score 0

82 1

62 2

80 3

58 4

72 5

73 6

65 7

66 74 9

62 The parameter of interest is the mean score /i in this population. The sample is an SRS of size n 4 drawn from the population. Because the students are labeled 0 to 9, a single random digit from Table B chooses one student for the sample.

(a) Find the mean of the 10 scores in the population. This is the population mean /x.

(b) Use the first digits in row 116 of Table B to draw an SRS of size 4 from tjhis population.

What are the four scores in your sample? What is their mean x ? This statistic is an estimate of ytt.

(c) Repeat this process 9 more times, using the first digits in rows 117 to 125 of Ta ble B. 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 /U ?