Data Session 9, Part D: The Effect of Sample Size

Session 9, Part D:
The Effect of Sample Size

In This Part: Sample Size 20 | Comparing Sample Sizes 10 and 20 | Box Plot Comparisons

In order to investigate whether samples of 20 sub-regions are more likely to produce better estimates than samples of 10 sub-regions, you will need to consider repeated sampling results for samples of size 20. Here is the stem and leaf plot for 100 estimates of sample size 10: Here is the stem and leaf plot for 100 estimates of sample size 20:


Problem D1
Compare the two distributions above. In particular, look at how many estimates for each fall in the interval 450 to < 550 (i.e., the 4H and 5L stems). What does this suggest about the effect of sample size on the accuracy of estimation?

Which distribution has more estimates "closer" to the actual answer of 500? Close Tip

Problem D2

Now let's revisit our table of intervals.

a.	Use the 100 estimates from samples of size 20 to determine the proportion of estimates in each of the intervals.

Interval	Interval Length	Proportion of Estimates in Interval

		Sample Size 10	Sample Size 20

350-650	300	100/100	100/100
375-625	250	98/100	100/100
400-600	200	94/100	98/100
425-575	150	84/100	94/100
450-550	100	69/100	83/100
475-525	50	37/100	55/100

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b.	Compare the proportions within the six intervals for the two different sample sizes. What does this suggest about the effect of sample size on the accuracy of the estimation procedure?

In summary, as the sample size increases, the distribution of the estimates becomes more concentrated. Consequently, a larger sample size generally improves the accuracy of the estimation procedure.

Next > Part D (Continued): Box Plot Comparisons

Session 9: Index | Notes | Solutions | Video