A- 90% A 91-98% A+ 100%

B- 80% B 81-88% B+ 89%

C- 70% C 71-78% C+ 79%

D- 60% D 61-68% D+ 69%

F 0-58% F+ 59%

40 points possible

Mean: 82.5Mean: 80%

Reminder: Grades are averaged, not raw scores.

Next Exercise…

Survey 1

(Go to Homework Link)

Due by Wednesday, 5pm.

Where are we now?

Still learning how to draw conclusions based on the data that was collected from an experiment…

Confidence Intervals(aka "margin of error")

The current mean GPA of college students nationwide is 2.65 and the standard deviation (σ) is 0.5.

What would be the mean GPA of (all) college students if universities were all free?

Study: Randomly sample 100 high school students, let them choose any university to attend for free. Calculate their mean GPA scores after 4 years.

EXACT Hypothesis: Mean GPA of ALL free university students is 2.65.

95% Confidence Interval Example

100 5.0 9.2 nX

100

5.0*29.2 * 2

nX

0.31.09.2

100

5.0*29.2 * 2 -

nX

8.21.09.2

)0.3 , 8.2( :answer

95% Confidence Interval Example

100 5.0 9.2 nX

)0.3 , 8.2( :answer

This interval does not “CONTAIN” the EXACT Hypothesis (2.65). Therefore, REJECT the EXACT Hypothesis.

Hypothesis TestingQuantitative DV

• Hypothesis: the average (mean) CalPoly student studies 3 hours per day outside of class time.

• Run Experiment (Observe n Cal Poly students).

• Compute the 95% confidence interval. Obtain, e.g., (2.5, 2.9).

• If the hypothesized value is outside the interval, REJECT the hypothesis. Otherwise, do not reject it (keep quiet).

• Unfortunately, this method is not always possible, so we need a more general approach…

Hypothesis Tests

Step 1: Name Change…

Your Research Hypothesis will now be called your “Alternative Hypothesis”.

Your EXACT hypothesis will now be called your “Null Hypothesis”.

Example

• Question: Are Dogs Smarter (or Dumber)

than Cats?

• Testable alternative hypothesis:

IQ dogsIQ dogs ≠ ≠ IQ catsIQ cats

• Independent variable: Animal Type

• Dependent variable: IQ score

Notice that the Notice that the

NULL HYPOTHESIS,NULL HYPOTHESIS,

HH0 0 :: IQ dogsIQ dogs = = IQ catsIQ cats

or, Hor, H0 0 :: IQ dogsIQ dogs - - IQ catsIQ cats = 0 = 0

and the and the

ALTERNATIVE HYPOTHESIS,ALTERNATIVE HYPOTHESIS,

HH1 1 :: IQ dogsIQ dogs ≠ ≠ IQ catsIQ cats

Or, Or, HH1 1 :: IQ dogsIQ dogs - - IQ catsIQ cats ≠ 0≠ 0

Refer to POPULATION PARAMETERS, not SAMPLE Refer to POPULATION PARAMETERS, not SAMPLE STATISTICS!!!STATISTICS!!!

Note: this will be on the next exam.Note: this will be on the next exam.

Notice that the Notice that the

NULL HYPOTHESIS,NULL HYPOTHESIS,

HH0 0 :: IQ dogs IQ dogs - - IQ catsIQ cats = 0 = 0

and the and the

ALTERNATIVE HYPOTHESIS,ALTERNATIVE HYPOTHESIS,

HH1 1 :: IQ dogsIQ dogs - - IQ catsIQ cats ≠ ≠ 00

CANNOT BOTH BE TRUE!!!CANNOT BOTH BE TRUE!!!

When you make your When you make your decision, what can happen?decision, what can happen?

Your ConclusionYour Conclusion

Fail to Fail to Reject the Reject the NullNull

Reject the Reject the NullNull

RealityReality

Null TrueNull True Type IType IErrorError

Null FalseNull False Type IIType IIErrorError

If, in reality, If, in reality, Dogs are smarter than Dogs are smarter than Cats Cats (on average),(on average),

Which Which TwoTwo Can Happen? Can Happen?

Your ConclusionYour Conclusion

Fail to Fail to Reject the Reject the NullNull

Reject the Reject the NullNull

RealityReality

Null TrueNull True

Null FalseNull False Type IIType IIErrorError

1 2

3 4

Examples of Null Hypotheses

HH0 0 :: = = 4.54.5

HH0 0 :: 1 1 = = 2 2

oror

HH0 0 :: 1 1 - - 2 2 = 0= 0

150X 15000s

01.021 XX 0000000001.0s

Alternative Hypotheses

HH1 1 :: > > 4.54.5

HH1 1 :: 1 1 < < 2 2

((Or Or HH1 1 :: 1 1 - - 2 2 < < 00))

HH1 1 :: 4.54.5

HH1 1 :: 1 1 2 2

"Directional" or "One-tailed""Directional" or "One-tailed"

"Non-Directional" or "Two-tailed""Non-Directional" or "Two-tailed"

A clinical psychologist hypothesizes that phobias are more common in industrialized countries than in underdeveloped countries. In this case, the alternative hypothesis is: a. directional b. non-directional  c. uni-directional d. bi-directional 

A clinical psychologist hypothesizes that phobias are more common in industrialized countries than in underdeveloped countries. In this case, the alternative hypothesis is:  

IndustNonIndust XXHa : . 0

IndustNonIndust XXHb : . 1

IndustNonIndustHc : . 0

IndustNonIndustHd : . 1

IndustNonIndust XXHe : . 0

IndustNonIndust XXHf : . 1

IndustNonIndustHg : . 0

IndustNonIndustHh : . 1

A clinical psychologist hypothesizes that phobias are more common in industrialized countries than in underdeveloped countries.

If then a. Reject the null hypothesis. b. Fail to reject the null hypothesis. c. Reject the alternative hypothesis. d. Not enough information. 

, IndustrialNonIndustrial XX