HOT SEAT

Question #1 What three general conditions (or assumptions) do you need to check before you perform inference? Random, Normal, Independent

Question #2 What three things should you include in your “STATE” when you are going to perform a significance test? Hypotheses, significance level, parameter

Question #3 How do you check for the Normal condition when a proportion is your parameter of interest? np and n(1-p) ≥ 10

Question #4 You always have to check for independence, but when do you have to check the 10% rule? When sampling without replacement!

Question #5 What are the three things you must include when you are “concluding” a confidence interval? Confidence level, interval, and the parameter (captures the true population’s…)

Question #6 What are the two main calculations in the “DO” part of a significance test? Test statistic and the P-value

Question #7 When checking the Normal condition for an inference method involving mean, you can assume the condition is met if the sample size is large enough – how large does it have to be? Greater than or equal to 30.

Question #8 Choose a following answer: Which of the following is NOT true about P-values? It gives us the chances of our sample results given that the null hypothesis is true. It allows us to make a decision to reject or fail to reject the null hypothesis. The P stands for the “Power” value Given what type of test we are using, we can use either Table A, Table B, or the graphing calculator to find this value.

Question #9 What is the parameter of interest? An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. p = proportion of adults who are in favor of the ban

Question #10 What type of test would you use for this problem? (give the entire method name) An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. One sample z test for a population proportion

Question #11 What would a Type I error be in this case? An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. We would reject that half of the adults favor the ban when actually half of the adults do favor the ban.

Question #12 The power of a test is .88, what does this mean? That there is an 88% chance that we will reject the null hypothesis when the null was false. Alternative answer: That there is a 12% chance of a Type II error

Question #13 State the hypotheses for this problem: Athletes performing in bright sunlight often smear black grease under their eyes to reduce glare. Does eye black work? In one experiment, 16 randomly selected student subjects took a test of sensitivity to contrast after 3 hours facing into bright sun, both with and without eye black. Here are the differences in sensitivity, with eye black minus without eye black: 0.07 0.64 -0.12 -0.05 -0.18 0.14 -0.16 0.03 0.05 0.02 0.43 0.24 -0.11 0.28 0.05 We want to know whether eye black increases sensitivity on average. H0: µd = 0 and Ha: µd > 0

Question #14 He needs to draw a graph! Athletes performing in bright sunlight often smear black grease under their eyes to reduce glare. Does eye black work? In one experiment, 16 randomly selected student subjects took a test of sensitivity to contrast after 3 hours facing into bright sun, both with and without eye black. Here are the differences in sensitivity, with eye black minus without eye black: 0.07 0.64 -0.12 -0.05 -0.18 0.14 -0.16 0.03 0.05 0.02 0.43 0.24 -0.11 0.28 0.05 We want to know whether eye black increases sensitivity on average. See Cody’s work below, what is he missing when he checked the Normal condition? Normal: Although the sample size is small (less than 30), I will assume this is roughly Normal because it is unimodal and symmetric. He needs to draw a graph!

Question #15 A random sample of 100 likely voters in a small city produced 59 voters in favor of Newt Gingrich. The observed value of the test statistic for testing the null hypothesis: H0: p = 0.5 versus the alternative hypothesis Ha: p > 0.5 is a) b) c) d) e)

Question #16 Given a H0: µ = 0; Ha: µ ≠ 0 and from data has a and with a sample size of 18. Assuming that the conditions are met, Sara calculated the test statistic and used her calculator function tcdf(1.20, 100, 17) = .123. Why is her P-value not 12.3%? - Because she needs to double .123 to become 0.247!

Question #17 Name three ways to increase the power of a test. Increase α, decrease β, increase sample size