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Parameters VS. Statistics and Samples & Census How do we compare statistics and parameters? M2 Unit 4: Day 3 Statistics VS Parameters Statistics (for samples) : x and S Parameters (for populations) : and Today… You will be given the population parameters and You will be given a data set for a sample and you will find the statistics x and S Then you will compare the statistics to the parameters Example1 For a large population, the mean = 25.1 and the s.d =5.3. A random sample produced the following data values: 25, 21, 32, 14, 17, 22, 29. Compare the mean and s.d of the random sample to the population parameters. Sample x 22.86 S x 6.36 Population 25.1 x 5.3 The mean of the sample is less than population mean while the s.d. of the sample is greater than the population s.d. Example 2 For a large population, the mean = 4.8 and the s.d =3.6. One random sample produced the following data values: 5, 1, 3, 4, 7, 6, 8, 2, 1, 3. Compare the means and s.d’s of the random samples to the population parameters. Sample 1 x4 S x 2.45 Population 4.8 x 3.6 The mean and standard deviation of the sample are less than population mean and the population s.d. Example 3 For a large population, the mean = 12.3 and the s.d =4.24. One random sample produced data values of 21, 13, 15, 12, 20, 22, 16, 18. Another random sample produced data values of 14, 15, 12, 20, 29, 18. Compare the means and s.d’s of the random samples to the population parameters. The mean of the both Sample 1 Sample 2 x 17.13 S x 3.72 x 18 S x 6.10 Population 12.3 x 4.24 samples are greater than population mean. The s.d. of the 1st sample is less than that of the population s.d while the s.d. of the 2nd sample is greater than the population s.d. Example 4: Compare Statistics and Parameters Population 18.4 x 15.6 Gillian Ted x 17.8 S x 12.35 x 21.1 S x 14.52 less than greater than less than Example 5: Compare Statistics and Parameters A teacher wants to know how often her students study at night. Random samples are collected from John and Sally, two students. Their results are given below. The population mean is 1.24 and the population standard deviation is about 2.32. Compare the means and standard deviations of the random samples to the populations parameters. John: .35, 1.23, .55, 2, 3.1 Sally: 1.1, .46, 2.3, .25, 2.2 John Sally x 1.45 S x 1.13 x 1.26 S x 0.96 x 2.32 Population The mean of the both samples are 1.24 greater than population mean. The standard deviations of both samples are less than that of the population standard deviation. Comparing A Population and A Sample A population is a group of people or objects that you want information about • “ the whole”, everything or everyone which is relevant A sample is a subset of the population • “the part”, just a piece of the population Example: ECHS student survey • sample = 1 student from each class • population = all the students in the school Example: Each week, the Gallup Poll questions about 1500 adult US residents to determine national opinion on a wide variety of issues. What is the population? Population = all US residents that week Who is the sample? Sample = 1500 US residents questioned Random Sample A sample in which each member of the population has an equal chance of being selected. Examples: Putting everyone’s name in a hat and pulling one out. Having a computer randomly generate a list of items. Representative samples A) B) C) A principal wants to know if teachers would be willing to give $1.00 each week to help provide new text books for the students. Which would give a representative sample? Ask teachers who have first period planning Ask the teachers that want new text books in their classrooms Ask teachers as they sign in each morning Representative random samples The following list provides the average number of cookies baked for a bake sale. A food inspector wants to choose samples of cookies to inspect. Choose a method of random selection that is Joe 20 representative of all cookies. Sally 12 Jane 28 A) choose the first cookie baked by each person B) choose at random, 2 cookies from each person C) choose at random, 5 cookies from Joe, 3 cookies from Sally and 7 cookies from Jane Representative random samples The following list provides the average number of tshirts made by a t-shirt company. The manager wants to choose samples of t-shirts to inspect. Choose a method of random selection that is Black 1500 representative of all t-shirts. White 1250 Red 1000 A) choose 5 black t-shirts, 10 white and 50 red B) choose at random, 30 Black shirts, 25 White shirts and 20 Red shirts C) choose at random, one of each shirt Samples Unbiased vs. Biased Unbiased (FAIR) Sample: A representation of the population you want information about. Biased Sample: A sample that over represents the population or under represents part of the population. Examples: 1. A pharmacy wants to find out if its customers would be interested in ordering their prescription through their website. Asking every third prescription customer if they would be interested would be an ______ unbiased sample. 2. A movie theater wants to know which day of the week its customers prefer to see movies. A biased sample would be to ask the question to all of its customers on Thursday. Examples: 3. A school is trying to find out what is the favorite sport among the students. Asking every other football player, “What is your biased sample. favorite sport?” would be a 4. A store wants to know which style of jeans customers prefer. An unbiased sample would be to ask every other customer what their favorite style of jeans is. Census Every individual in the population is contacted • not really practical because they are very time consuming and extremely costly. Example: • the US does a census every 10 years. It tries to contact everyone in the US and asks them questions about race, ethnicity, # of people in their house hold, etc. The next census will occur in 2020. Assignment: Pg. 275 # 6 – 8, 11 Pg. 276 # 1, 2, 4 – 6