Click to edit Master title style A-90%A91-98%A+100% B-80%B81-88%B+89% C-70%C71-78%C+79% D-60%D61-68%D+69% F0-58%F+59% 40 points possible Mean: 82.5 Mean:

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Click to edit Master title style A-90%A91-98%A+100% B-80%B81-88%B+89% C-70%C71-78%C+79% D-60%D61-68%D+69% F0-58%F+59% 40 points possible Mean: 82.5 Mean: 80% Reminder: Grades are averaged, not raw scores.

Click to edit Master title style Next Exercise… Survey 1 (Go to Homework Link) Due by Wednesday, 5pm.

Click to edit Master title style Where are we now? Still learning how to draw conclusions based on the data that was collected from an experiment…

Click to edit Master title style 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.

Click to edit Master title style 95% Confidence Interval Example

Click to edit Master title style 95% Confidence Interval Example This interval does not “CONTAIN” the EXACT Hypothesis (2.65). Therefore, REJECT the EXACT Hypothesis.

Click to edit Master title style Hypothesis Testing Quantitative 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…

Click to edit Master title style 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”.

Click to edit Master title style Example Question: Are Dogs Smarter (or Dumber) than Cats? Testable alternative hypothesis:  IQ dogs ≠  IQ cats  IQ dogs ≠  IQ cats Independent variable: Animal Type Dependent variable: IQ score

Click to edit Master title style Notice that the NULL HYPOTHESIS, H 0 :  IQ dogs =  IQ cats or, H 0 :  IQ dogs -  IQ cats = 0 or, H 0 :  IQ dogs -  IQ cats = 0 and the ALTERNATIVE HYPOTHESIS, H 1 :  IQ dogs ≠  IQ cats Or, H 1 :  IQ dogs -  IQ cats ≠ 0 Refer to POPULATION PARAMETERS, not SAMPLE STATISTICS!!! Note: this will be on the next exam.

Click to edit Master title style Notice that the NULL HYPOTHESIS, H 0 :  IQ dogs -  IQ cats = 0 and the ALTERNATIVE HYPOTHESIS, H 1 :  IQ dogs -  IQ cats ≠ 0 CANNOT BOTH BE TRUE!!!

Click to edit Master title style When you make your decision, what can happen? Your Conclusion Fail to Reject the Null Reject the Null Reality Null True Type I Error Null False Type II Error

Click to edit Master title style If, in reality, Dogs are smarter than Cats (on average), Which Two Can Happen? Your Conclusion Fail to Reject the Null Reject the Null Reality Null True Null False Type II Error 12 34

Click to edit Master title style Examples of Null Hypotheses H 0 :  = 4.5 H 0 :  1 =  2 or H 0 :  1 -  2 = 0

Click to edit Master title style Alternative Hypotheses H 1 :  > 4.5 H 1 :  1 <  2 ( Or H 1 :  1 -  2 < 0 ) H 1 :   4.5 H 1 :  1   2 "Directional" or "One-tailed" "Non-Directional" or "Two-tailed"

Click to edit Master title style 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

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

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.