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Parent Guide

Chapter 13 builds on the statistical ideas of Chapter 2 and the probability ideas of Chapter 12 to show how to make predictions.

Inferential statistics

Making predictions about a large group from a smaller group is called inferential statistics. One of the most familiar examples of inferential statistics is polling; it?s impossible to survey everyone, so only a sample is polled and the results are generalized to the whole group, or population. The validity of the generalization depends on how well the smaller sample represents the population. One way to get a representative sample is by using a random process.

After choosing a sample randomly, someone trying to describe the full population must describe the sample, using statistics studied in Chapter 2. These include measures of central tendency, such as mean and median, and measures of spread, such as standard deviation. They also include a new idea: the shape of the data?generally, the degree to which the data are symmetric to the mean.

The third step in making predictions about the population is to decide how confident you are that the sample statistics match the corresponding numbers in the population. Polling results are often reported as being ?accurate to within 4 points.? To make decisions about what it means to be ?accurate? and what interval is associated with that degree of accuracy, your student will think about what would happen if many random samples were taken.

Bivariate statistics

Sometimes you want to make predictions about one characteristic of a population based on another characteristic. For example, you might want to predict the height of an oak tree based on its circumference. Here, students collect data about two characteristics and find ways of describing their correlation?either through a correlation coefficient or graphs.

Summary problem

From the sample census data on age and income, what can you conclude about the population?

Age and Income

Age (yr)Income ($)
316000
430
4835,000
50
4160,000
3765,970
2120
503000
3568,400
4822,330
100
7436,636
3244,000
548500
5427,000
4250,125
16600
4531,300
3834,500
7718,000
4663,058
20
6765,568
3350,592
5480,000
        
Age (yr)Income ($)
160
140
44106,000
80
5636,868
4220,000
396500
6135,000
19750
222400
4017,000
2710,090
2215,000
3872,000
3951,000
300
361500
40
221561
3752,523
236000
4015,462
3124,634
30
4287,500

Questions you might ask in your role as student to your student:

  • What is the population from which this sample was taken?
  • What do you think the mean age of the population is?
  • What?s a 95% confidence interval for that age?
  • How confident can you be that the mean income of the population is $19,000?
  • How well do age and income correlate?

Sample answers