1. Stat 301 – Day 28 Review

2. Last Time - Handout (a) Make sure you discuss shape, center, and spread, and cite graphical and numerical evidence, in context. Variable = ratio, quantitative Parameter = mean ratio in population,  To test H 0 :  =.10 vs. H a :  <.10, would use a one-sample t-test.

3. Power… 1. What values of the sample mean would reject the null hypothesis?

4. Power… How often reject the null hypothesis when  =.09?

5. Handout Variable = whether or not ratio is below.10 Parameter = proportion of population with ratio below.10,  H 0 :  =.5, H a :  >.5 (most Cal Poly students carry less than 10% of body weight)

6. Handout But if more than half of the students carry less than.10, what does that tell you about the median ratio? Less than.10.

7. Power… How often will we reject H 0 :  =.5 when  =.6?

8. Why is the power lower?

9. Exam 2 – Ch. 3, Ch. 4 Focus: Generalizing from sample back to population 1) How do we select a good sample? 2) How do we obtain a p-value comparing our sample statistic to a hypothesized population value? Ho/Ha Sampling distributions/Normal probability model Test statistic/p-value 3) How do we estimate the population parameter based on the observed statistic? Margin-of-Error/Confidence interval/Confidence

10. Types of problems Sample selection issues  Including nonsampling errors  Bias vs. precision (representative vs. accuracy) Normal probability distribution calculations Sampling distributions  Checking and applying CLT (sketch!), calculating probabilities of statistic values from known population Inference problem  Assess evidence vs. estimate parameter  Interpretations, properties, what if?, validity

11. Terminology cautions Percentage vs. proportion (vs. number of) Bias vs. precision (vs. representative, accurate) Number of samples vs. sample size Duality: Values in a C% confidence interval will not be rejected at the (100-C)/100 level of significance for a two-sided alternative Confidence vs. significance Statistical vs. practical significance  How assess strength of evidence?  How assess size of difference?

12. Exercise 51/52 Exercise 51: CLT says if you take lots of random samples from this population, the distribution of sample means will be approximately normal with mean equal to 18.2 and standard deviation equal to Exercise 52: take lots of random samples from this population Calculate probabilities Count the number of values in each region

13. Advice Same as before (e.g., pretend closed book) Practice drawing well-labeled sketches Words to avoid: It, Proof, Data Words to only use when you mean it: probability, confidence, significant, random Work out problems from scratch  Practice setting up (what is step 1?)