Winter, 2010 Wednesday, Feb. 3Stat 217 – Day 14Central Limit Theorem, cont.Variation of Activity 13-3 (p. 261)As reported in the journal Nature (2003), German bio-psychologist Onur Güntürkün conjectured that the human tendency to turn right manifests itself in other ways as well, so he studied kissing couples to see whether they tended to lean their heads to the right while kissing. He and his researchers observed couples from age 13 to 70 in public places such as airports, train stations, beaches, and parks in the United States, Germany, and Turkey. They were careful not to include couples who were holding objects such as luggage that might have affected which direction they turned. They observed a total of 124 kissing couples.(a) Define the parameter of interest in this study (in words) and indicate the symbol used to denote the number.(b) Suppose for now that one-half of all kissing couples lean to the right. What does this conjecture imply about the parameter?(c) In the sample of 124 couples, 80 leaned their heads to the right. Is this number a parameter or a statistic? Explain. Also indicate what symbol is used to denote it.The key inference question is whether it is surprising to obtain a (random) sample resultat least this extreme if there was no right turning tendency with kissing in the population. Now that we know the sample size, we can use an applet to approximate the sampling distribution of all such samples with n = 124 from this population with = .5. You can actually use either the Reese’s Pieces applet or the Coin Tossing Applet:(d) Does the sample result of 80 out of 124 turning right seem surprising?Winter, 2010 Wednesday, Feb. 3(e) Alternatively, we could use the Central Limit Theorem, which would predict the sampling distribution of sample proportions from samples of size n = 124 from a population with = .5:Shape:Mean:Standard deviation:(e) Are these predictions consistent with the applet results?(f) So how far is the observed sample proportion from our conjecture for the population proportion? (Hint: Think z-score)(g) How often does the normal probability model predict such a sample proportion, or more extreme (in the direction conjectured by the researchers), would occur through random sampling error alone?(h) Based on this sample, assuming it’s representative of the larger population of kissing couples, does .5 appear to be a reasonable guess for the proportion of this population of kissing couples that turns to the right? Explain.(i) What about = 2/3? What about = .75?To turn in: Activity 15-1The answer to (f) is .1562 (or about .16 as predicted by the Empirical Rule as
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