Winter, 2012 Wednesday, Jan. 18Stat 217 – Day 9Two-sided tests, Normal approximationNew Ideas from Lab 2:- We can consider a population proportion as the parameter of interest ( )- We can state two-sided alternative hypotheses (e.g. H0: .5)- In many situations, we can use a mathematical model, the normal distribution, to appropriate the p-value of a test (large sample size)Example 1: Most people are right-handed and even the right eye is dominant for most people. Molecular biologists have suggested that late-stage human embryos tend to turn their heads to the right. In a study reported in Nature (2003), German bio-psychologist Onur Güntürkün conjectured that this tendency to turn to the right manifests itself in other ways as well, so he studied kissing couples to see which side they tended to lean their heads while kissing. Dr. Güntürkün noted that about 2/3 of people have a dominant right foot, or eye, and conjectured that people would exhibit a similar tendency of “right sidedness” when kissing. He and his researchers observed 124 couples in public places such as airports, train stations, beaches, and parks. They were careful not to include couples who were holding objects such as luggage that might have affected which direction they turned. For each couple observed, the researchers noted whether the couple leaned their heads to the right or to the left. (a) Identify the observational units and the variable of interest.Obs Units: Variable:(b) Identify the sample and population of interest in this study.Sample:Population:(c) Identify the parameter of interest in this study.(d) The researchers observed 80 of the 124 couples leaned to the right. Calculate the statistic.(e) Suppose you want to investigate whether the sample data provide evidence that the population proportion of all couples who lean their heads to the right while kissing ( ) is different from .6667. Statethe corresponding null and alternative hypotheses.H0:Ha:(f) Before we use an applet to find a p-value, what is the applet going to do? What can you predict about the applet results in advance/?Winter, 2012 Wednesday, Jan. 18(g) Use the Reese’s Pieces applet to determine whether there is statistically significant evidence that the probability of a kissing couple turning to the right differs from 2/3. (h) Would the normal approximation be valid for this study? How are you deciding? What is the approximate p-value using the normal distribution?(i) Is the p-value small enough to reject the null hypothesis at the .05 level of significance? What does this imply? State your conclusion in the context of the study.(j) Does this mean we have proven that = 2/3?(j) How could we determine whether .70 is a plausible value for ?(k) Are any other values plausible for ? Can you find them all?Key Idea: A 95% confidence interval for reveals the range of plausible values for the population parameter by finding all the values that are not rejected in a two-sided test of significance with a 5% level of significance.(l) Are you convinced that more than half of all kissing couples lean to the right?
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