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

Solution  

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?


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Which distribution has more estimates "closer" to the actual answer of 500?   Close Tip

 

Problem D2

Solution  

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

375-625

250

98/100

400-600

200

94/100

425-575

150

84/100

450-550

100

69/100

475-525

50

37/100

show answers


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


hide answers


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

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