1. Stat 217 – Day 7
Tests of Significance

2. Last Time
Using observed sample data to evaluate a claim about the general process
Is this convincing evidence that, in general, students tend to put Tim on the left?
Idea: Look at results that do happen “by chance alone” to see whether our observed data are consistent with that pattern

3. Example 1: Helper/Hinderer
Trying to decide between
1. Infants do evaluate individuals as appealing or aversive based on their actions
2. Infants don’t have a genuine preference and these 16 just happened to pick the helper toy more often

4. If infants are picking at random
Meaning choose equally between the two toys in the long run
“could have been results”

5. Conclusions
Small p-value : It would be very unlikely to have 14 (or more) picking the helper toy if all 16 infants were picking blindly between the two toys
Conclusion: Strong evidence against the null hypothesis in favor of the alternative
Strong evidence these infants (in the long run) have a genuine preference for the helper toy

6. Follow-up study
Video

7. Example 2: Bottled water vs. Tap water
Let p represent the probability that some one picks tap water as their favorite
Null hypothesis: p = .25 (people pick the tap cup equally among the four cups)
Alternative hypothesis: p < .25 (people are less likely to prefer tap water than non-tap)

8. Tap water
What are typical values for the proportion of successes (tap water) if people are choosing equally?

9. Tap water
If people pick tap water 25% of the time in the long run, then we would expect to see 11.1% or fewer picking water in about 5% of repetitions of 27 water tasters by chance alone.
A p-value of .05 is some evidence that the long-run probability of picking tap water is less than .25.
Tap water is “statistically significantly” less preferred.

10. “Survey”
A campus legend tells the story of two friends who told their professor that they got a flat tire returning to town and missed the exam. The professor agreed to give them a make-up exam.
The first question (worth 5 points) was easy, but the second question worth 95 points, asked “Which tire was it?”

11. Data Collection
If you have to choose a hypothetically flat tire, which of the four tires would you say went flat? Left front Right front Left rear Right rear

12. To Do Submit Lab 1 by beginning of next class
Finish reading Section 1.2