5.27 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 10 scholarship players currently on your women’s basketball team. For convenience, the 10 players have been labeled with the integers 0 to 9. For each player, the total amount of time spent (in minutes) on Twitter during the last week is recorded in the following table.
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| Player | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Total time (min) | 98 | 63 | 137 | 210 | 52 | 88 | 151 | 133 | 105 | 168 |
The parameter of interest is the average amount of time on Twitter. The sample is an SRS of size n = 3 drawn from this population of players. Because the players are labeled 0 to 9, a single random digit from Table B chooses one player for the sample.
(a) Find the mean for the 10 players in the population. This is the population mean μ.
(b) Use Table B to draw an SRS of size 3 from this population. (Note: You may sample the same player’s time more than once.) Write down the three times in your sample and calculate the sample mean . This statistic is an estimate of μ.
(c) Repeat this process nine more times using different parts of Table B. Make a histogram of the 10 values of . You are approximating the sampling distribution of .
(d) Is the center of your histogram close to μ? Explain why you’d expect it to get closer to μ the more times you repeated this sampling process.