Download - HYPOTHESIS TESTING: A FORM OF STATISTICAL INFERENCE Mrs. Watkins AP Statistics Chapters 23,20,21
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HYPOTHESIS TESTING: A FORM OF STATISTICAL INFERENCE
Mrs. WatkinsAP Statistics
Chapters 23,20,21
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What is a hypothesis test?
• Hypothesis Testing: Method for using sample data to decide between 2 competing claims about a population parameter (mean or proportion)
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What question do such tests answer?
Is our finding due to chance or is it likely that something about the population seems to have changed?
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Why Statistical Inference?
The only way to “prove” anything is to use entire population, which is not possible.
So, we use INFERENCE to make decisions about a population, based on a sample
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EXAMPLE:
• A new cold medicine claims to reduce the amount of time a person suffers with a cold. A random sample of 25 people took the new medicine when they felt the onset of a cold and continue to take it twice a day until theyfelt better. The average time these people took the medication was 5.2 days with a standarddeviation of 1.4 days. The typical time a person suffers with a cold is said to be one week.
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Questions from our cold study:
What is the difference between the population mean and the sample mean? 1.8 days
Is this difference likely to be due to chance?
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How could we compute how likely it is to see a mean of 5.2 when we are expecting a mean of 7 days? Use a z score!
z = 7 – 5.2_ = 6.43 1.4/√25
probability of this is nearly 0…so unlikely
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Hypotheses: Ho: μ = 7 (the status quo of cold duration)Ha: μ < 7 (what we hope to be true about the
new medication)
Our evidence suggests that Ha is more likely to be true.
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Writing Hypotheses:
Statistical Hypothesis: a claim or statement about the value of the population parameter
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2 Hypotheses:• Null Hypothesis: claim that is assumed to be
true—usually based on past research Noted Ho
• Alternative Hypothesis: competing claim based on a new sample suggesting that a change has occurred Noted Ha
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Kinds of Tests:
Two tailed: Ho: μ = 7Ha: μ ≠ 7
Right tailed: Ho: μ = 7 Ha: μ > 7
Left tailed: Ho: μ = 7 Ha: μ < 7
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Hypotheses Example 1:
A medical researcher wants to know if a new medicine will have an effect on a patient’s pulse rate. He knows that the mean pulse rate for this population is 82 beats per minute:
Ho: μ = 82
Ha: μ ≠ 82
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Hypotheses Example 2:
A chemist invents an additive to increase the life of an automobile battery. The mean lifetimes of a typical car battery is 36 months.
Ho:μ = 36Ha:μ > 36
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Hypotheses Example 3:
An educational research group is investigating the effects of poverty on elementary school reading levels. Prior research suggests that only 46% of children from poor families achieve grade level reading by third grade
Ho: p = 0.46Ha: p ≠ 0.46
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Hypotheses Example 4:
A cancer research team has been given the task of evaluating a new laser treatment for tumors. The current standard treatment is costly and has a success rate of 0.30.
Ho: p = 0.30Ha: p > 0.30
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Statistical Significance:
The results of an experiment or observational study are too “different” from the established population parameter to have occurred simply due to chance….
Something else must be going on…..
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ASSIGNMENT:
Now go on-line and watch this video carefully for good example of hypothesis testing in use: http://www.learner.org/courses/againstallodds/unitpages/unit25.html
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α = rejection region
α is the rejection region on the normal curve, accepted to be the highest probability that cause you to uphold the Ho.
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RESULTS OF HYPOTHESES TESTS
Let’s assume α = 0.05.If p < α, then we reject Ho.
The sample result is too unlikely to have happened due to chance, so the Ho is overturned.
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If p > α, then we fail to reject Ho.The sample result could have
happened due to chance, so the Ho is upheld.
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What does p value mean?
The p value is the probability (based on z or t curve) of seeing a sample mean of this value or more extreme if the Ho is really true.
If p value is low, then the Ho must not be true. The sample data suggests that the status quo has changed.
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Conclusions of Hypothesis Tests
Rejecting Ho = Statistically significant change
Failing to reject Ho=Difference between sample mean and Ho mean was not statistically significant.
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Testing about MeansWhen investigating whether a claim about a MEAN is correct, you have to decide whether to do a t test or a z test.
Z test: if you know pop. standard deviationT test: if you know sample standard deviation
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HYPOTHESIS TESTS
H: HypothesesA: AssumptionsT: Test and Test StatisticP: P valueI: Interpretation of p valueC: Conclusion
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HYPOTHESIS TESTING FOR PROPORTIONS
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EXAMPLE
A newspaper article from 5 years ago claimed that 9.5% of college students seriously considered suicide sometime during the previous year. If a sample from this year consisted of 1,000 students and 144 claimed that they had seriously considered suicide, is there evidence to suggest that the proportion has increased?
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DRAW THE MODEL OF THE SAMPLING DISTRIBUTION OF THE PROPORTION
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Hypotheses
Null Hypothesis: Ho : p = 0.095(the stated claim about the population
proportion)Alternative Hypothesis:
Ha: p > 0.095Ha: p < 0.095Ha: p ≠ 0.095
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Z Proportion Test
There are no t tests for proportions, only z.Note that we are using p not for standard deviation of distribution.
Test Statistic: z = P value: use normal cdf
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Assumptions:
1. Random Sample or Random Assignment2. Large enough to assume normal model:
n p > 10n q > 10
Note that we are using p not for verifying normality assumption.
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EXAMPLE: DO HATPIC
An educator claims the dropout rate in Ohio schools is 15%. Last year, 280 seniors from a random sample of 2000 seniors withdrew from school.
At α = 0.05, can the claim of 15% be supported or is the proportion statistically significantly different?
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