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Interactive Reading Assignment Guide Section 8.1 Introduction Screen 1: This is a review problem on the different sampling techniques (systematic, convenience, cluster, stratified, simple random. Go back to section 1.3 if you need a refresher. Screen 2: This problem focuses on determining the population and/or the sample mean from a data set. Go back to section 3.1 if you need a refresher. Screen 3: This problem focuses on determining the population and/or the sample standard deviation from a data set. Go back to section 3.2 if you need a refresher. Screen 4: This problem focuses on calculating probabilities using the normal probability calculator. Go back to section 7.1 & 7.2 if you need a refresher. Screen 5: List of Objectives. Also a brief statement about how we can approximate the population mean using different sampling techniques and referencing the “sampling distribution.” Screen 6: The screen shows the definitions of a sampling distribution. Objective 1: Describe the Distribution of the Sample Mean: Normal Population Screen 1: The video on this screen demonstrates how we can find a “sampling distribution” using a computer simulation. The sampling distribution is the distribution that is created by taking multiple samples from the same population. Screen 2: This screen demonstrates how to find the mean and standard deviation of a sampling distribution. Here is what you need to know: ̅’s (sample means) is the same as 1. The mean of the sampling distributions for all of the 𝒙 the mean of the population. 𝝁𝒙̅ = 𝝁 ̅’s (sample means) is the 2. The standard deviation of the sampling distribution for all of the 𝒙 sample as the standard deviation of the population divided by the square root of n. 𝝈𝒙̅ = 𝝈 √𝒏 Screen 3: This screen shows how to use the formulas (above) to approximate the mean and standard deviation of a sampling distribution. Screen 4: This screen states that the shape of the sampling distribution of 𝑥̅ is normal, if the population is normal. Developed by Sharleen McCarroll in conjunction with the textbook Interactive Statistics: Informed Decisions Using Data, by Michael Sullivan III & George Woodbury, 2016. Screen 5: This activity allows you to simulate taking multiple samples from a population that has a normal distribution. Screen 6: This question asks you information about the sampling distribution for 𝑥̅ . This information was covered on the previous screens. You only get ONE attempt on this problem. Screen 7: Example 1. This example demonstrates how to find the probabilities for a sampling distribution. Watch the STAT CRUNCH video. Screen 8: This problem is like the problem in example 1. Be sure to use Stat Crunch. Objective 2: Describe the Distribution of the Sample Mean: Non-Normal Populations. Screen 1: The video on this screen demonstrates how we can find a “sampling distribution” from a non-normal population using a computer simulation. The sampling distribution is the distribution that is created by taking multiple samples from the same population. Screen 2: On this screen you will find the Central Limit Theorem, which is an important Theorem in Statistics. Watch the “In Other Word” video. Scree 3: This screen describes how large your sample size should be in order to assume that the distribution for 𝑥̅ to be normal. As a general rule, we will use a sample size of 30 or greater to be enough in order to assume that 𝑥̅ has a normal distribution. (In practice, your sample size may have to be larger than 30, but we will use 𝑛 ≥ 30 for the rest of this class.) Screen 4: On this screen, you will find an illustration of a population with three different samples taken from the same population. You should notice that as n gets larger, the sampling distribution starts to look more like the symmetric or bell-shape. Screen 5: General rule of thumb for using the Central Limit Theorem. (You should try to remember these rules.) Screen 6: Activity 1. This activity will allow you the opportunity to generate many different sample from a population. You can see the population distribution, the sample distribution (for 1 sample), and the sampling distribution of sample means (the distribution for all of the 𝑥̅ ’s). Screen 7: This question is based off your conclusions from the activity. Be careful – you only get one chance on this question. Screen 8: Example 2. This example demonstrates how to calculate probabilities and z-scores for sample means. You should watch the “by hand” so you understand the process and the Stat Crunch video solutions. Screen 9: This problem is like the problem on the previous screen. Screen 10: This is a great summary video. Be sure to watch this video. Screen 11: End of Section.