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CH 7: Sampling Distributions AP Statistics 12 7.1 – What is a Sampling Distribution? Consider this Scenario: Suppose Judy takes a sample of 1000 subjects from the population of BC voters. She will obtain a statistic that she will use to make an inference about the parameter of interest; that is, the proportion of BC voters who will vote NDP in the next election. The distribution of the sample is 462 yesses and 538 noes. She repeats the same sampling process 9 more times to obtain a total of 10 SRS’s of size 1000 from the population. She then calculates the average number of yesses and noes to generate the sampling distribution of yesses and noes, which turns out to be 483 and 517, respectively. She uses this data to make inferences about the parameter. Use the scenario above to create your own definition of all of the words in bold. Sample Population Statistic Parameter Inference Distribution of the Sample Sampling Distribution
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CH 7: Sampling Distributions AP Statistics 12
7.1 – What is a Sampling Distribution? Consider this Scenario: Suppose Judy takes a sample of 1000 subjects from the population of BC voters. She will obtain a statistic that she will use to make an inference about the parameter of interest; that is, the proportion of BC voters who will vote NDP in the next election. The distribution of the sample is 462 yesses and 538 noes. She repeats the same sampling process 9 more times to obtain a total of 10 SRS’s of size 1000 from the population. She then calculates the average number of yesses and noes to generate the sampling distribution of yesses and noes, which turns out to be 483 and 517, respectively. She uses this data to make inferences about the parameter. Use the scenario above to create your own definition of all of the words in bold. Sample Population Statistic Parameter Inference Distribution of the Sample Sampling Distribution
CH 7: Sampling Distributions AP Statistics 12
Q: An opinion poll asks the question “Are you afraid to go outside within a kilometer of your home because of crime?.” Suppose that the proportion of all adults who would say “Yes” to this question is p = 0.4
a) Use Line 120 of a random number table to simulate the result of an SRS of 20
adults. What proportion of “Yeses” did you obtain? Call this answer p̂ . Is p̂ a
statistic or a parameter?
b) Now, repeat the process 4 more times using consecutive lines of random
number table. Find p̂ for each of these samples.
c) Now, find the mean of your p̂ ’s . Is this answer the mean of a sample or is it the
mean of the sampling distribution?
d) If you could repeat this process an infinite number of times, what do you expect would happen to your answer from (c)?
Notes: Ultimately, we want to be able to use a sample statistic to estimate a parameter. For this to happen, we need to reduce bias and reduce variability in the sampling distribution. Bias can be eliminated through careful sampling and variability can be reduced through increasing sample size. Bias: Variability:
