Download Hypothesis Testing

HL Stats Option
Confidence Testing
Warm Up 3.25.15
NO CALCULATOR
Hypotheses
• Statistical Hypothesis – statement about the value
of a population parameter. Ex. The mean or
proportion
• Null Hypothesis H0 – parameter takes on a definite
value, meaning no effect occured. Ex. That
population mean μ has value μ0
– Assumed True
• Alternative Hypothesis H1 – Alternative to the Null
Hypothesis. Ex. There is a difference between μ
and μ0
Example Situation
• Mr. Gilmartin’s roommate is testing the effect of a drug
on response time by injecting 100 rats with a unit dose
of the drug, subjecting each to neurological stimulus,
and recording its response time. He knows that the
mean response time for rats not injected with the drug
is 1.2 seconds. The mean of the 100 injected rats is
1.05 with a sample standard deviation of 0.5 seconds.
Do you think that the drug has an effect on response
time?
• Determine the Null and Alternate Hypotheses
• How would you test your hypotheses?
One vs. Two Tailed
• One-Tailed:
– H1: μ > μ0
– H1: μ < μ0
• Two Tailed
– H1: μ ≠ μ0
• Could be > OR <
1 v. 2 Example
• Using the example below create the Null
hypothesis along with a the situation for
each type of alternate hypotheses:
Banana Boat is testing a new sun block
and wants to compare it to its old sun
block that on average provided 5 hours of
protection
Error Types
• Type I – the mistake of rejecting the Null
Hypothesis when it is in fact true
• Type II – the mistake of accepting the Null
Hypothesis when it is not true
Normal Distribution
X~N(μ,σ2)
“X is Normally distributed with mean μ and
variance σ2.”
Z Score
•
• For our sample X~N(μ0,σ2/n)
• Called the Null Distribution
Critical Region
• To reject a Null hypothesis we typically
look for a 5% level of significance or lower
based on the normal distribution curve we
call the area that would reject the Null
Hypothesis the critical region and the
values the critical values
Two Tailed Test
• If we are looking at a two-tailed test (recall
μ0 ≠ μ) we know that there is a 95%
confidence interval as shown below:
Two-Tailed
• As a result the critical regions and values for a
two-tailed test are as follows:
• If our μ0 is in the critical region we reject the Null
Hypothesis as our μ0 has <5% likelihood of
occurring.
• This also means the probability of a Type I Error is
< 0.05
One-Tailed Test
• See if you can create the Normal
Distribution Curve and find the critical
regions (at 5% significance) for both:
– One-tailed (right) test
– One-tailed (left) test
• Explain how you found your critical values
One Tailed (Right) Test
• To find critical values we need
P(Z≥k)=0.05 so k≈1.645
*Note – Level of
significance
determines the
critical region
and values
One Tailed (Left) Test
• To find critical values we need
P(Z≤k)=0.05 so k≈-1.645
Critical Regions (General)
p-Value
Decision Making
• We reject the Null Hypothesis if any of the 3
checks below hold true:
1. Test statistic is in the critical region
2. p-value is strictly less than a
3. Value is in the critical region
• If we do not reject the Null then we accept it.
– Note: Does not mean we have proven the Null
Hypothesis, rather we don’t have enough
evidence to reject it
Hypothesis Testing in
7 Steps
Example
Check-in
• Try the 6 problems on your worksheet
Homework
• Complete Terminology Worksheet
• Part 1 and 2 of Study Guide
Hypothesis Testing
(Know σ)
• If no effect then mean of the sample
should be the same as the mean of
population sample
• Standard deviation of sample should =
standard deviation of population / square
root of sample