Module 4 Sampling Population

Population

Sample

Populations: what we want Samples: shortcuts EXAMPLE 1: Robotics team Population

2 32110121041

Variable

Sample Statistics:

Population parameters:

Mean-

Mean-

Standard Deviation-

Standard Deviation-

*census: “ask everybody”

SYMBOLS Quantative Variables Categorical

Population (parameter)

mean Standard deviation proportion

Sample (statistic)

Types of Sampling A. Simple Random Sampling • Everyone has an equal chance of getting selected • Results are predictable How? • Random number generator 1. Billy 7.Andrew 2. Jamie 8.John 3. Sue 9. Nina 4. Barnie 10. Christina 5. Jack 11. Jeremy 6. Mary 12. Meredith B. •

Calculator MATH PRB randInt(start #, end #)

Step 1: Set up proportion Step 2: Randomly select that number in an SRS of that Stratified Random Sampling There are problems with simple random sampling and people having certain opinions, so you strata(option) Step 3: Repeat for each strata can use stratified random sampling How many should I ask?

EXAMPLE: 9th

Grade Frequency 9th 120 th 10 150 th 11 130 th 12 180 11th C. Systematic Sampling •

Every __th person



People walking into store

10th

STEPS: 1.

2.

3.

4.

12th

D. Cluster Sampling 1. identify equally sized groups 2. Use SRS to choose entire cluster(s) for sample Cluster

Watch video on sampling: doing it wrong to have Mr. Pethan explain how sampling can go wrong.

MODULE 5 Confidence Intervals

Goal- find how precise our guess really is by imagining what most other guesses look like Bootstrapping • Take sample and replicate it many times • Best guess of population • “We are now 95% confident that the proportion of Americans that think Munchkin is cuter than Peno is between 45% and 75%” Bootstrapping Confidence Intervals of Means • __________ summarize categorical data o What proportions of Americans think Munchkin is cuter? • __________ summarize quantative data o What is the average weight of 7 week old Goldendoodle pups in USA? EXAMPLE: Goldendoodle Pups Sample Average: 7.1 lbs Are we content with this average? No, we need a bootstrap *USE STATKEY! Click on Confidence Interval for a Mean, Median, Std. Dev. Enter sample data and click away on generate 10000 samples button

Instead of saying 7.1 lbs, we can now say: We are ___% confident that the average weight of Standard Goldendoodle puppies at 7 weeks old is between___and___lbs

Watch next 2 videos to get a really good understanding of stat key and the components of it Larger Samples Make Smaller Intervals • Interval shrinks at 1/(square root of sample size change) • Sample is 4x largeràinterval is____ the size • Sample is 100x largerà interval is ____size

Confidence Intervals: +/- and interval notation • +/- notation starts with middle and says how much it varies in each direction Interval Notation Middle “Wiggle Room” +/- notation

45 to 75% (45+75)/2= 60% 75-60=15%

Interval Notation Middle “Wiggle Room” +/- notation

6.8 and 7.4 lbs (6.8+7.4)/2= 7.1 lbs 7.4-7.1= .3

Explaining in Context Confidence level: 95% confident Interval: 45%-75%

In context, we said: We’re ___% confident that the proportion of Americans that think Munchkin is cuter than Peno is between _____% and _____%.

In context, we said: We’re ___% confident that the proportion of Americans that think Munchkin is cuter than Peno is between _____% +/- _____%. We are ___ than 95% confident that more Americans think Mucnhin is cuter than Peno. Results become less meaningful when the good sampling conditions are not met: -SRS or equivalent - low under coverage -low non-response EXAMPLE 1: Question Population Type Result

Assuming a good sample, you can say:

I am ___% confident that the proportion of Americans that approve of the president is between ____% and ____%. I am ___% confident that the proportion of the President is ____% +/ - ____.

EXAMPLE 2: Question Population Type Result I am ___% confident that the average number of apps A is between ____% and ____%. Assuming a good sample, you can say: I am ___% confident that the average number of apps a Byron students has

on their iPad is ____ +/- ____apps.

Module 6 Hypothesis Testing

Court of Law null hypothesis: alternative hypothesis: EXAMPLE: Skittles Null hypothesis: Alternative: What is convincing? *Run it through STATKEY Setup the Problem Define the parameter to test Create Hypotheses Find the level that evidence is convincing

Answer the Question Collect random sample Simulate and find p-value Conclusion

Logic of a Test EXAMPLE: Does mentioning a specific appetizer increase the total sales of appetizers? Null Hypothesis Alternative Hypothesis

Readers found an average of 45 errors in an essay by Jack McConnell. Would they find more errors in the exact same essay by Hsaoi-Ping Zhang? Parameter Null Hypothesis Alternative Hypothesis Alpha Cut-off Probability

That guy’s average fairway shot with a 3 wood goes 214 yards. Would he hit it a diff distance with a 3 iron?

Parameter Null Hypothesis Alternative Hypothesis Alpha Cut off Probability

37% of customers order a large coffee. Does rephrasing “what size would you like” to “do you want a large” make more peple buy a large coffee? Parameter Null Hypothesis Alternative Hypothesis Alpha Cut off Probability

Review of Hypotheses Null hypothesis: no difference

Alternative Hypothesis: up/ down/different

p= .04

p> .4 p< .4 p=.4

Mean

Proportion

Watch next two videos to learn how to use STATKEY for these types of problems

TYPE 1 and TYPE 2 ERRORS Type 1

• Rejecting null hypothesis when it was right • Convicting an innocent person • Ex: Probability: α (such as 0.5)

Type 2 • Accepting null hypothesis when it was wrong • Not convicting a guilty person • Probability : β EXAMPLES: I did a study at the significance level a=.01. My p-value was .008. Despite this very low p-value, my null hypothesis later turned out to be correct. -Is there an error? If so, what type?

Null: patient is HEALTHY Alternative: patient has DISEASE Type 1 Error: Type 2 Error: Which is worse in this situation?

Module 4

Every __th person. •. People walking into store. Calculator. MATH ... number of apps A is between ____% and ____%. I am ___% confident that the average.

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