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LP5.6.7ConfidenceIntervalsMOE.notebook

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May 21, 2018

Warm Up:


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May 21, 2018

Population Proportion...I wish it was called the population ratio because it is defined as...

the part of the population with a particular attribute, expressed as a fraction, decimal, or percentage of the population


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May 21, 2018

INDUCED Variability vs. NATURAL Variabilitycreated because of the treatment the subject was placed in

just because people, animals, plants, etcetera, are naturally different

Differences in Sample Means population mean =

sample mean =In a classic experiment, two or more treatment groups are randomly created and then subjected to the different treatments. We need to be able to determine if the variability in the groups is due to the treatment.

The mean of the sample means is EQUAL to the population mean


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May 21, 2018

confidence- established when we can determine if a sample can from a given population, and quantify how likely it is to happen

Sample Means & Sample Proportions


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May 21, 2018

WARM UP - Suppose the prom committee has to choose a theme. The expectation is that 50% of the class would have to approve of the theme for it to be accepted.

The committee does not have time to survey the whole class so they survey a sample of 20 random students instead. 8 out the 20 students in the survey liked the theme.

Should they reject the theme based on this data?


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May 21, 2018

In order to answer this question we will run a simulation of 100 samples

of 20 students assuming a 50% average rate of approval for the prom

theme.

NOW what do you think? Does a result of 8 seem like it is out of the ordinary if we wanted the average survey to be 10?


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May 21, 2018

What we're doing is called...

confidence interval- a range of values that contain 95% of the data (approximately 2 standard deviations around the mean)

So to answer the question...

NO, they should not reject the theme because their sample survey result of 8 out of 20 students lies within a 95% confidence interval of the desired population of the mean of 50%.


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May 21, 2018

The state passing rate on the Algebra 1 CC Regents last year was 65%, so that is the population proportion. South Central HS had a passing rate of 72%. They claim that their result is exceptional.

South Central's rival East Side HS has a brilliant data coordinator who runs a simulation to see if SCHS is indeed getting "exceptional" results in mathematics. The simulation assumes an average of 65 and is run 200 times. The results of the simulation are shown in the dot plot below:

There are 200 dots here, so 95% of them

would be all but the outer most 10 dots.


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May 21, 2018

A dot plot or table will always be provided for you to do this analysis on the Regents. You DON'T need to run the simulation yourself.

Inferential statistics is never about proving beyond any doubt that a population.

168/256 = .71 30/52=.58

as a sample size increases the range in the distribution of the sample will likely also increase...just a note...


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May 21, 2018

I created a simulation using the population mean to determine if our sample was typical (within the 95% confidence interval) or not typical.

This shows that the sample

mean of 57% is outside of

the 95% confidence interval.

That means that there is a difference that is statistically significant between the sample of

sophomores and the population of juniors with regard to cell phone ownership.


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May 21, 2018

Let’s say we have a population with a 0.25 proportion of being 65 years or older. If researchers surveyed 50 people walking out of a movie and found that 21 of them were 65 years or older, do you believe this sample came from the general population with a p=0.25? Why or why not.

[The simulation shown below was run 200 times with a sample size of 50 assuming the population proportion of 0.25 to assist you in answering the question.]

Note: Finding the sample proportion is not necessary here b/c the axis is measured in number of people.


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May 21, 2018

Historically, the proportion of emperor penguins with adult weights above 60 pounds is 0.64. Take this to be the population proportion for this characteristic.

(a) A sample of 26 emperor penguins in a zoo found that 20 of the penguins had adult weights above 60 pounds. Calculate the sample proportion for this sample.

Below is a simulation run 100 times with a sample size of 26 using the population proportion listed above.

(b) Do you have enough evidence from the simulation to conclude that penguins raised in a zoo have a significantly higher proportion of weights above 60 pounds? Why or why not?


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May 21, 2018

Janua

ry 2

017

Rege

nts


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May 21, 2018

August 2016 Regents


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May 21, 2018

August 2016 Regents

Warm Up


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May 21, 2018

Margin of Error

standard error-

BUT...we commonly use the 95% confidence interval, so how many standard deviations is that???

when one standard deviation of the set of sample statistics is used for the margin of error (gives about a 68% confidence interval)

We've worked specifically with 95% confidence intervals, but we can determine any confidence interval by doing

A higher confidence interval requires a larger margin of error

Estimate ± Margin of Error

margin of error- expresses the amount of random sampling error in a survey's results


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May 21, 2018

Stephen's Beverage Company is considering whether to produce a new brand of cola. The company will launch the product if at least 25% of cola drinkers will buy the product. Fifty cola drinkers are randomly selected to take a blind taste-test of products A, B, and the new product. Nine out of fifty participants preferred Stephen's new cola to products A and B. The company then devised a simulation based on the requirement that 25% of cola drinkers will buy the product. Each dot in the graph shown below represents the proportion of people who preferred Stephen's new product, each of sample size 50, simulated 100 times.

Assume the set of data is normal and the company wants to be 95% confident of its results. Does the sample proportion obtained from the blind taste-test, nine out of fifty, fall within the margin of error developed from the simulation?

The company decides to continue developing the product even though only nine out of the fifty participants preferred its brand of cola in the taste-test. Describe how the simulation data could be used to support this decision.

Notice:when the sample size increases, the margin of error decreases


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May 21, 2018

Augu

st 20

16 R

egen

ts


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May 21, 2018

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