A pre-election survey of 100 prospective voters shows 55 in favor of Candidate A.
We know that approximately 2% of women develop breast cancer between the ages of 50- and 54. Suppose we find 32 incident cases of breast cancer in a sample of 1000 women between the ages of 50- to 54. These women are the daughters of women who had breast cancer.
An study by an 11-year old girl made headlines for challenging the validity of therapeutic touch (Rosa et al., 1998). In therapeutic touch, the touch therapists' hands are passed over a patient's body without actually touching the patient, supposedly to manipulate human energy fields. In the current experiment, touch therapists rested their hands, palm up, on a flat survace approximately 25 to 30 cm apart. To prevent the experimenter's hands from being seen, a tall, opaque screen with cutouts at its base were placed over each subject's arm, and a cloth towel was attached to the screen and draped over the therapists' arms. Each therapist underwent a test of 10 trials in which the experimenter (the 11-year-old girl) hovered her right hand, palm down, 8 to 10 cm above one hand of the therapist and then said "Okay." The touch therapist then stated which of his or her hands was nearer to the experimenter's hand. Each subject was permitted to take as much or as little time as necessary to make each determination. Results are as follows:
No. correct (out of 10) | Frequency | Frequency * No. Correct |
0 | 0 | 0 |
1 | 1 | 1 |
2 | 1 | 2 |
3 | 8 | 24 |
4 | 5 | 20 |
5 | 7 | 35 |
6 | 2 | 12 |
7 | 3 | 21 |
8 | 1 | 8 |
9 | 0 | 0 |
10 | 0 | 0 |
Total | 28 | 123 |
Notice that this study found that touch healers were able to detect the presence of the experimenter in 123 out of 280 trials. However, let us view each of the above 28 trials as a cluster (e.g., one cluster showed a results of 1 of 10, one cluster showed a results of 2 of 10, and so on). We want to calculate a 95% confidence interval for the proportion of "successes." To do this, we must calculate the design effect (deff) attributable to the clustered sample.
Describe Compare Study Sample Probability Setup
-[_]------------------------------------------------------
Clust Num Den Num Den Num Den Num Den
No. 1 1 10 13 4 10 25 7 10 37 0 0
No. 2 2 10 14 4 10 26 7 10 38 0 0
No. 3 3 10 15 4 10 27 7 10 39 0 4
No. 4 3 10 16 5 10 28 8 10 40 0 0
No. 5 3 10 17 5 10 29 0 0 41 0 0
No. 6 3 10 18 5 10 30 0 0 42 0 0
No. 7 3 10 19 5 10 31 0 0 43 0 0
No. 8 3 10 20 5 10 32 0 0 44 0 0
No. 9 3 10 21 5 10 33 0 0 45 0 0
No.10 3 10 22 5 10 34 0 0 46 0 0
No.11 4 10 23 6 10 35 0 0 47 0 0
No.12 4 10 24 6 10 36 0 0 48 0 0
Global variance : 0.000880
Cluster variance : 0.000988
Design effect : 1.12
In a laboratory investigation of the teratogenicity of an agent, we find malformed pups in 12 out of 85 lab rat litters.
Smoking cessation programs have modest success in helping their clients stop smoking. A study of 234 smokers who had expressed a desire to stop smoking recorded the number of days each client successfully restrained from smoking (variable DAYS).
Data, below, represent diastolic blood pressure measurements in a sample of 50 men. Let diastolic blood pressure 95 mm Hg represent hypertension. Calculate the prevalence of hypertension in the sample and a 95% confidence interval for the prevalence of hypertension in the population from which this sample was drawn.
94 94 82 100 112 110 84 78 92 112
94 92 86 84 90 72 88 92 88 84
98 98 84 90 90 70 80 90 80 106
74 95 100 94 84 70 102 92 84 80
84 86 98 82 80 88 80 84 100 86
In a report of adult dental health in 25- to 34-year-old English women showed 20 of 262 women with edentition (missing teeth).
In a study of physical and sexual abuse during childhood, Brown and Anderson found 166 people with histories of abuse in a sample of 947 psychiatric patients.
Suppose we observe 3 events (cancers, side-effects, bad outcomes, "whatever") in a population, and would like to know whether this occurrence is significant. What additional information would you need to make a judgement under such circumstances?
Suppose you are suspicious that a coin is "unfair" (i.e., that it doesn't turn up an equal number of heads and tails upon flipping). In particular, you are suspicious that the coin turns up heads more than it should. To test this problem, what would your null and alternative hypotheses be? Would you use a one-sided or two-sided alternative? (This, in a way, will say a lot about your philosophy.) How many times would you flip the coin? Carry out an experiment to test a coin.