CHAPTER 15 #1-13
1. Parametric tests (such as t or ANOVA) differ from nonparametric tests (such as chi-square) primarily in terms of the assumptions they require and the data they use. Explain these differences.
3. In a study, a pair of faces is shown on a screen and the reasearchers record the amount of time the baby spends looking at each face. In a sample of n=40 infants, suppose that 26 spent the majority of their time looking at the more attractive face and only 14 spent the majority of the time looking at the unattractive face. Is this result significantly different from what would be expected if there were no preference between the two faces? Test with a=.05.
5. Research has demonstrated that people tend to be attracted to others who are similar to themselves. One study demonstrated that individual are disproportionately more likely to mary those with surnames that begin with the same letter as their own. The researchers began by looking at marriage records and recording the surname for each groom and the maiden name of each bride. From these records it is possible to calculate the probability of randomly matching a bride and a groom whos last names begin with the same letter. Suppose that this probability is only 6.5%. Next, a sample of n=200 married couples is selected and the number who shared the same last initial at the time they were married is counted. The resulting observed frequencies are as follows:
SAME INITIAL: 19
DIFFERENT INITIAL: 181
Do these data indicate that the number of couples with the same last initial is significantly different than would be expected if the couples were matched randomly? Test with a=.05.
6. Suppose the researcher from the previous problem repeated the study of married couples initials using twice as many participants and obtaining observed frequencies that exactly double the original values. The resulting data are as follows:
SAME INITIAL: 38
DIFFERENT INITIAL: 362
6A. Use a chi-square test to determine whether the number of couples with the same last initial is significantly different than would be expected if couples were matched randomly. Test with a=.05.
6B. You should find that the data lead to rejecting the null hypothesis. However, in problem 5 the decision twas fail to reject. How do you explain the fact that the two samples have the same proportions but lead to different conclusions?
9. The color red is often associated with anger and male dominance. Based on this observation, Hill and Barton monitored the outcome of four combat sports (Boxing, Tae Kwan Do, Greco-Roman wrestling, and freestyle wrestling) during the 2004 Olympic games and found that participants wearing red outfits won significantly more often than those wearing blue.
9A. In 50 wrestling matches involving red vs. blue, suppose that the red outfit won 31 times and lost 19 times. Is this result sufficient to conclude that red wins significantly more than would be expected by chance? Test at the a=.05 level of significance.
9B. In 100 matches, suppose red won 62 times and lost 38. Is this result sufficient to conclude that red wins significantly more than would be expected by chance? Again, use a=.05.
9C. Note that the winning percentage for red uniforms in part A is identical to the percentage in part B (31 out of 50 is 62%, and 62 out of 100 is 62%). Although the two samples have an identical winning percentage, one is significant and the other is not. Explain why the two samples lead to different conclusions.
12.Research has demonstrated strong gender differences in teenagers approaches to dealing with mental health issues. In a typical study, eighth-grade students are asked to report their willingness to use mental health services in the event they were experiencing emotional or other mental health problems. Typical data for a sample of n=150 students are shown in the following table.
WILLINGNESS TO USE MENTAL HEALTH SERVICES
Probably No Maybe Yes Total
Males 17 32 11 60
Females 13 43 34 90
Total 30 75 45
Do the date show a significant relationship between gender and willingness to seek mental health assistance? Test with a=.05.
13. Research indicates that playing a prosocial video game tends to increase prosocial behaviors. In a similar experiment, participants were assigned to play a prosocial, a violent (antisocial), or a neutral video game. Near the end of each session, the experimenter accidentally spilled a box of pencils on the floor and then recorded whether the participant stopped to help pick them up. The data are as follows:
Did Not Help: 3
Total, prosocial: 15
Did not Help: 8
Total, violent: 15
Did Not Help: 7
Total, neutral: 15
Did Not Help:18
Do the data indicate a significant relationship between the type of game played and helping behavior? Test with a=.05.
Female family member has to get in vitro fertilization. Doctors say she's got a 10% chance of each fertilized egg becoming viable and that the odds of each is independent from the odds of the rest being successful. To reckon the odds that at least one will take, I took the odds of all failing (each being 1.0-0.1=0.9) for 1-0.9^4=0.3439 or 34%. There's a wrinkle.
She's a hard-core, but not insane, pro-lifer: any viable fertilized egg is a life that cannot be murdered. Thus, doing six eggs runs the risk of too many kids; too few wrecks the odds of a successful kid; and the procedure is freakin' expensive.
IIRC, I can figure out the odds of each possible set of successes & failures using the binomial expansion, but I'm not sure I remember how to do it. If she's doing four eggs, is this the proper way to figure out the odds of 0 successes, 1 success,...,4 successes?
(.1+.9)^4 = .1^4 * .9^0 + 4(.1^3 * .9^1) + 6(.1^2 * .9^2) + 4(.1^1 * .9^3) + .9^4
where each term is the odds of that number of successes & failures. So for (success, failure):
(4, 0) = .0001 or .01%
(3, 1) = .0036 or .36%
(2, 2) = .0468 or 4.68%
(1, 3) = .2916 or 29.16%
(0, 1) = .6561 or 65.61%
Which, if I'm adding correctly, doesn't quite add up to 100%, but is close enough, I guess.
Have I done this correctly? If so, I simply use the expansion for the fifth- and sixth-powers for five or six eggs, correct?
Please let me know ASAP! I just found out about this tonight, and she really wanted to know how all the probabilities worked out, and I think it's important to know. I only have a couple of days to give all this to her, so please let me know. She may be a hard-core pro-lifer, but I want to help her be the smartest one she can be! ^_^
Thank you so much!!!
Has anyone conducted the Gustav Fechner experiment
, asking people which of 10 rectangles is most appealing to them?
Did you get the same results, with the most appealing being 5:8, the closest of the 10 to the Divine Proportion? What was your sample size?
, I'm going to try it out this week because I'm very curious to see if after 100+ years, results are the same!
dear members of community, i need your help a lot!
the problem is - i can't find any info on topic
"theory of divisibility in the ring of polynomials with TWO variables and their usage"
i've looked through all catalogues of our uni library but in vain, there is only one Russian book which is not enough for my research.
if you can advise relevant links on free e-materials or send me the scanned books on topic (email@example.com), i'll be very-very grateful!
THANKS IN ADVANCE!
Nov. 21st, 2007 @ 05:41 pm
I've just joined this community today. I'm doing my ph.d. in number theory, specially in elliptic curves.
Is anyone interested in this subject?
|» I need some math motivation!|
i'm starting to get deeper and deeper into the trigonometry side of my pre-cal/trig class and UGH
those identities are driving me crazy and i don't want to start hating math lol. I'm a total math nerd (hence the reason why i am using my summer to take pre-cal so i can take AP Calculus my junior year), i just need help with these damn identities.
anyone want to help?
lol, trig is fun, i mean, who doesn't enjoy graphing cosine and sine graphs? but these identities are a pain
i feel stupid for posting this, but i'm really not sure where else i could ask.|
i loved maths up until year 11. sure i complained about it, but i was good at it. (hell, i passed year 11 maths without doing any work in class or at home.) ... that sounds like i'm bragging. i'm not. sorry. anyway. that year i had a maths teacher who while good at what he taught had at some point lost any love for it. the result being he did not want to make extra work for himself with the student who wanted to know more about everything, wanted to know why on it all. he was very discouraging and in the end i just gave up. i dropped maths after that year despite the fact that i could easily have gone further. and i never did any real maths again. and now looking back i wish i had. i've lost skills i had and treasured. and to be honest i'm not even sure what i've lost and what i still remember. (sob story end, question start)
what i'm wanting is a "non threatening" way of finding that out and maybe relearning some of it. maths games etc that go from about beginning of high school up.
crossposted to my own LJ.
|» Applications to Lagranges theorem in group theory|
Hello all mathlovers! I'm a student at Uppsala University in Sweden and i'm writing on my thesis in educational mathematics. The highlight if it is Lagranges theorem in group theory and I'm intrested in anything that is worth to know about it! Curiosa, applications etc...|
Does anyone know where I might find such information?
|» (No Subject)|
Hey fellow math lovers! I'm a sophomore in a truly tiny math program at a rather small college over here in New York.|
In about a week and a half I'm flying halfway across the country to attend the Nebraska Conference for Undergraduate Women in Mathematics. So I was wondering, and I'm sorry if this shouldn't be up here or something (you can delete it in that case), is anyone on here going? Just trying to connect with anyone who might be going. =)