review hw: e1 a) too high. polltakers will never get in touch with people who are away from home...
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Review HW: E1
• A) Too high. Polltakers will never get in touch with people who are away from home between 9am and 5pm, eventually they will eventually be dropped from the sample. Because these are the people who are less likely to have children under the age of 5 at home the same will contain an artificially high percentage of children under 5 at home.• B) Adults are more likely to be at home during dinnertime then during
the day• C) Sampling bias due to the problem being with the design of the
survey
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Review HW: E3
• Convenience sample resulting in sampling Bias• Students who take statistics are more likely to like math (HAHAHAHA)• Estimate will tend to be too high IF stat class is voluntary and “about
right” if it is a require class
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Review HW: E5
• <40 yr old would expect to get an estimate that is too high since that’s higher than average age• Too high - Since Rhode Island is so small and NE states so close
together
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Review HW E7
• A) Voluntary Response Sample• B)No, volunteer samples are typically biased with stronger feelings
one way or the other.• C)”Quite a bit less than 92%”. Voluntary response bias inflated
response
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Review HW E9
• Too high • a) families with no children don’t get to take the sample• b) families with many children are overrepresented
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4.2 Random Sampling: Playing It Safe by Taking Chances
• Understand the two main reasons for relying on chance to choose samples
• Learn the definition of a simple random sample• Recognize and implement several kinds of probability samples
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Probability Sample
• Occurs when each unit in a population has a fixed probability of ending up in the sample.• Used to randomize a survey
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Simple Random Samples
• All possible samples of a given fixed size are equally likely. All units have the same chance of belonging to the sample, all possible pairs of units have the same chance of belonging to the sample, all possible triples of units have the same chance, and so on.
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Steps in Choosing a Simple Random Sample1. Start with a list of all the units in the population2. Number the units in the list3. Use a random number table or generator to choose units from the
numbered list, one at a time, until you have reached the desired population size.
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Activity 4.2a Random Triangles – 20 min• Pg 232-234• Follow the steps listed in the activity
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PG 234 D11
• Describe how you could obtain a simple random sample of all students enrolled in the English classes at your school
Make a list of all English instructors. Get a roster for each class. Combine the list, delete repeats, then use a random digit table to select a sample
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PG 234 D11
• Readability. You’ve decided you must know the proportion of capital letters in this textbook because it can indicate the complexity of the sentences on a page. If the book is your population and each character is a unit. How could you get a simple random sample of 10k characters? What are the advantages and disadvantages of this sampling method?
Number the characters in the book. Use a computer or random #table to choose 10k numbers. The corresponding character go in the sample. Obviously, clearly inefficient.
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PG 241 P7
Decide whether these sampling methods produce a simple random sample of students from a class of 30 students. If not, explain why not.a) No – students at the end of the list do not get selectedb) No - sample size is not predetermined and not thus not simplec) No – all groups of students not chance of selection. 2 rowsd) Yese) No – not all groups; six girls cannot all be in sample.f) No – not all groups; students with last names different letters
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Stratified Random Samples
Sample created by breaking down a population into non-overlapping subgroups called strata. A sample of each subgroup must be a simple random sample.
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Why we want to stratify?
• Convenience – it is easier to sample in smaller, more compact groups than one very large group• Coverage – ensures all stratum are part of the sample• Precision – estimates are closer to the value of for the entire
population than with SRS aka less variability
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Steps to choosing a Stratified Random Sample1. Divide the units of the sampling frame unto non-overlapping
subgroups2. Take a simple random sample from each subgroup
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PG 237 D13
• An administrator wants to estimate the average amount of time high school students spend traveling to school. The plan is to stratify the students according to grade level and then take a simple random sample from each grade. What is the potentially good and what is potentially bad about his plan?
Good – time spent differs…more juniors and seniors with carsBad – Best stratum? What about by distance to school.
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Other Sampling Methods
• Cluster Samples – selecting an SRS of non-overlapping groups of units (called clusters) instead of individual units.• EX: Classrooms of students instead of individual students
Steps in Choosing a Cluster Sample1. Create a numbered list of all the clusters in your population2. Take a simple random sample of clusters3. Obtain data on each individual in each cluster in your SRS
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Two Stage Cluster Samples
• Variation of cluster sample• Choose clusters so that variation within each cluster reflects variation
in population. Then SRS from with only some of your clusters.Step in choosing a Two-Stage Cluster Sample1. Create a numbered list of all clusters in your population, and then
take a simple random sample of clusters.2. Create a numbered list of all the individuals in each cluster already
selected, then take an SRS from each cluster.
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Systematic Sample with Random Start1. Divide your population into groups of size you want for sample by a method such as counting off.2. Use a chance method to choose one of the groups for your sample
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Pgp 239 D15
• Why isn’t taking a systematic sample with random start equivalent to taking a simple random sample?
Two friends in line together at the time of counting wouldn’t both be in the sample
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PG 239 D18
• Both cluster sampling and stratified random sample involve viewing the sampling frame as a collection of subgroups. Explain the differences?• Stratified random sampling divides population into groups as different
as possible. • Cluster sampling tends to be used when people are stuck in groups
that are difficult to separate.
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4.2 Summary
• Simple Random Sample• Stratified random sample• Cluster sample• Two-stage cluster sample• Systematic sample with random start
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Pg 241-241
P8 – P11 & P13
HW: PG 242-243 #E15-17, E22