1). The TV show Myth Busters tried to determine if yawning was contagious. Adam
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Question
1). The TV show Myth Busters tried to determine if yawning was contagious. Adam Savage and Jamie Hyneman, the cohosts of Myth Busters, examined data from an experiment involving 50 subjects. Each subject was placed in a booth for an extended period of time and monitored by a hidden camera. Thirty-four subjects were given a “yawn seed” by one of the experimenters; that is, the experimenter yawned in the subject’s presence before leaving the room. The remaining 16 subjects were given no yawn seed. The table below shows the results:
Yawn Seed?
Subject Yawned?
Yes
No
Total
Yes
10
4
14
No
24
12
36
Total
34
16
50
The cohosts used the data to conclude that yawning is in fact contagious. Are they correct? Justify mathematically.
2). Does increasing the amount of calcium in our diet reduce blood pressure? Examination of a large sample of people revealed a relationship between calcium intake and blood pressure. The relationship was strongest for black men. Such observational studies do not establish causation. Researchers therefore designed a randomized comparative experiment.
The subjects in part of the experiment were 21 healthy men. A randomly chosen group of 10 of the men received a calcium supplement for 12 weeks. The control group of 11 men received a placebo pill that looked identical. The experiment was double-blind. The response variable is the decrease in systolic (heart contracted) blood pressure for subject after 12 weeks, in millimeters of mercury. An increase appears as a negative response.
Group 1- Calcium Group
7
-4
18
17
-3
-5
1
10
11
-2
Group 2- Placebo Group
-1
12
-1
-3
3
-5
5
2
-11
-1
-3
a). Is there significant evidence (alpha = 0.10) that the blood pressure is different for the calcium and placebo groups?
b). Perform a 90% confidence interval to estimate the difference in the mean decrease in blood pressure for the calcium and placebo populations.
c). Explain why your confidence interval in part b agrees with your decision in part a.
3). To determine whether or not caffeine dependence was a real phenomenon, E, Strain (“Caffeine dependence syndrome: evidence from case histories and experimental evaluation,” J. of Am. Medical Assoc., 272(1994), pp. 1604-1607) conducted a study in which 11 subjects were asked to perform a task twice-once under the influence of caffeine, and once under the influence of a placebo. The study measured how fast the subjects could repeatedly push a button when under the effects of the two treatments. The data is shown below. Button data is given in beats per minute the subject achieved. Do these data provide significance evidence that caffeine had a positive effect (increased) on the number of beats per minute?
Beats
Caffeine
281
284
300
421
240
294
377
345
303
340
408
Beats
Placebo
201
262
283
290
259
291
354
346
283
391
411
Difference
4). The number of grams of carbohydrates contained in 1-ounce servings of randomly selected chocolate and non-chocolate candy is listed below. Is there sufficient evidence to conclude that there is a difference between the variation in carbohydrate content for chocolate and non-chocolate candy? Use alpha = 0.05 level of significance.
5). Next perform a test to determine if the average number of carbohydrates in chocolate candy is greater than in non-chocolate. Use the 0.05 level of significance.
6). A study of chromosome abnormalities and criminality examined data from 4,124 males born in Copenhagen. Each man was classified as having a criminal record or not, using the registers maintained in the local police offices. Each was also classified as having the normal male XY chromosome pair or one of the abnormalities XYY or XXY. Of the 4,096 men with normal chromosomes 381 had criminal records, while 8 of the 28 men with normal chromosomes had criminal records. Some experts believe chromosome abnormalities are associated with increased criminality. Construct and interpret a 99% confidence interval for the difference in proportions.
Yawn Seed?
Subject Yawned?
Yes
No
Total
Yes
10
4
14
No
24
12
36
Total
34
16
50
Explanation / Answer
I will help you with #6 for the other questions please post it in a new question my friend :)
6). A study of chromosome abnormalities and criminality examined data from 4,124 males born in Copenhagen. Each man was classified as having a criminal record or not, using the registers maintained in the local police offices. Each was also classified as having the normal male XY chromosome pair or one of the abnormalities XYY or XXY. Of the 4,096 men with normal chromosomes 381 had criminal records, while 8 of the 28 men with normal chromosomes had criminal records. Some experts believe chromosome abnormalities are associated with increased criminality. Construct and interpret a 99% confidence interval for the difference in proportions.
P1 = 381 / 4096 = 0.094
P2 = 8/28 = 0.2857
P = ( 381+8) / 4124 = 0.094
alpha / 2 = 0.005 Z=2.57
I: 0.2857 - 0.094 +/- 2.57 * SRQT ( 0.094*0.906*(1/28 + 1/4096) )
0.1917 +/- 0.1422
0.0495 < P2 - P1 < 0.3339
WE ARE 99% THAT THE DIFFERENCE OF PROPORTION FOR OUR INFERECES IN BETWEEN 0.0495 AND 0.3339
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