1. Stat 217 - Day 16 Observations (Topic 16 and Topic 14)

2. Test of Significance (p. 338) 1) Define population parameter in words 2) State 2 competing claims about parameter null hypothesis H 0 : parameter = value alternative hypothesis H a : parameter or ≠ value 3) Check “technical conditions” for procedure 4) Calculate test statistic (assuming H 0 true) comparing what observed to what conjectured in H 0 5) Calculate p-value (see H a for “more extreme”) how often see sample data at least this extreme when H 0 true 6) Make a decision to either reject or fail to reject H 0 Is p-value small? State conclusion in context Compare p-value to “level of significance,  ”

3. Plausible Values.466 observed.25.3.4.5.6

4. Observations So we reject.25 and.3 and.6 as a plausible value for  but we fail to reject.4 and.5 as plausible values Another reminder that when you fail to reject the null, that doesn’t mean you have proven the parameter has that value. What is the set of all plausible values?  Which values of the parameter will we fail to reject based on our observed sample statistic?

5. The main idea Plausible values of the population parameter are values that are not “too far” from the observed sample statistic Say within 2 standard deviations  When CLT applies, 95% of sample proportions should fall within 2 standard deviations of the population proportion  So take your sample proportion and look 2 standard deviations on each side. 95% of the time, you will see the parameter….

6. Informal confidence interval for  (handout) Sample proportion – 2 SD Sample proportion + 2 SD SD( ) = Approximation for SD( ) = Calculate a confidence interval for the proportion of population that would choose right front tire Interpretation: I’m 95% confident that between 34.9% and 58.3% of population would pick RF But what does that mean?! “standard error”

7. Complete Activity 16-4 (p. 320-1)  Make your observations, we will discuss in class tomorrow Complete Part II  Make your observations, we will discuss in class tomorrow To turn in with partner:  What does it mean to say you are “95% confident”?  What happens to the sampling distribution of the sample mean when you increase the sample size? For Wednesday  Activities 16-3, 16-6 (with TOS applet)

8. For Wednesday  Activities 16-3, 16-6 (with technology)