Ch7 Sampling Distributions
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1 AP Statistics Name: Per: Date: Ch7 Sampling Distributions 7.1 What Is a Sampling Distribution? Read Parameters and Statistics Vocab: parameter, statistic How is one related to the other? Alternate Example: Identify the population, the parameter, the sample, and the statistic: (a) A pediatrician wants to know the 75th percentile for the distribution of heights of 10-year-old boys, so she takes a sample of 50 patients and calculates Q 3 = 56 inches. (b) A Pew Research Center Poll asked to 17-year-olds in the United States if they have a cell phone. Of the respondents, 71% said Yes. Read Sampling Variability Vocab: sampling variability, sampling distribution Why do we care? A father has four sons, with heights of 68, 71, 72, and 75 inches. Determine the sampling distribution of the sample mean height x for samples of size n = 2. 1
2 What is the difference between the distribution of the population, the distribution of the sample, and the sampling distribution of a sample statistic? Read Describing Sampling Distributions Vocab: unbiased estimator, biased estimator Provide some examples. How can you reduce the variability of a statistic? What effect does the size of the population have on the variability of a statistic? What is the difference between accuracy and precision? How does this relate to bias and variability? 2
3 7.2 Sample Proportions Read The Sampling Distribution of ˆp In the context of the Candy Machine Applet, explain the difference between the distribution of the population, the distribution of a sample, and the sampling distribution of the sample proportion. Based on the Candy Machine Applet and the Penny Activity, describe what we know about the shape, center, and spread of the sampling distribution of a sample proportion. When is it okay to say that the distribution of ˆp is approximately Normal? What are the mean and the standard deviation of the sampling distribution of a sample proportion? Are these formulas on the formula sheet? Are there conditions that need to be met for these formulas to work? 3
4 Read Using the Normal Approximation for ˆp Alternate Example: The superintendent of a large school district wants to know what proportion of middle school students in her district are planning to attend a four-year college or university. Suppose that 80% of all middle school students in her district are planning to attend a four-year college or university. What is the probability that an SRS of size 125 will give a sample proportion of at most 75%? 7.3 Sample Means Based on the penny activity, what do we know about the shape, center, and spread of the sampling distribution of a sample mean? Read The Sampling Distribution of x : Mean and Standard Deviation What are the mean and standard deviation of the sampling distribution of a sample mean? Are these formulas on the formula sheet? Are there any conditions for using these formulas? Read Sampling from a Normal Population What is the shape of the sampling distribution of a sample mean when the sample is taken from a Normally distributed population? Does the sample size matter? 4
5 Alternate Example: At the P. Nutty Peanut Company, dry-roasted, shelled peanuts are placed in jars by a machine. The distribution of weights in the jars is approximately Normal, with a mean of 16.1 ounces and a standard deviation of 0.15 ounces. (a) Without doing any calculations, explain which outcome is more likely: randomly selecting a single jar and finding that the contents weigh less than 16 ounces or randomly selecting 10 jars and finding that the average contents weigh less than 16 ounces. (b) Find the probability of each event described above. Read The Central Limit Theorem What is the shape of the sampling distribution of a sample mean when the sample is NOT taken from a Normally distributed population? Does the sample size matter? Does this concept have a name? Alternate Example: Suppose that the number of texts sent during a typical day by a randomly selected high school student follows a right-skewed distribution with a mean of 15 and a standard deviation of 35. Assuming that students at your school are typical texters, how likely is it that a random sample of 50 students will have sent more than a total of 1000 texts in the last 24 hours? 5
6 Chapter 7 Review Can you distinguish the following?,, p, n, x, pˆ, x, ˆ, x, ˆ p p Make a table comparing the distributions of x and ˆp (shape, center, spread, conditions) 6
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