STAT 110: Homework 4 (47 points) Group # and Names:
Due Sunday, September 18th
1. A standard test for extrasensory perception (ESP) asks subjects to identify which of four shapes (e.g., circle, square, diamond, or waves) is on the front of a card, viewed by the experimenter but not the subject. Suppose that a subject takes a test with 20 of these cards. We will focus on the number of correct identifications.
a. Explain why this is a binomial experiment by checking the required conditions.
(2 pts)
b. Use the binomial distribution (Excel linked to my website and mailed to you) to find the probability that a guessing subject would get 7 or more correct. (2 pts)
c. If a subject was to get 7 or more correct, would you believe they were really guessing or would you believe this was evidence for ESP? Explain. (2 pts)
d. Use the binomial distribution Excel file to find the probability that a guessing subject would get 9 or more correct. (2 pts)
e. If a subject was to get 9 or more correct, would you believe they were really guessing or would you believe this was evidence for ESP? Explain. (2 pts)
f. Suppose you had your supposedly psychic friend guess the shape on 50 cards. How many would they have to get correct before you would believe that they actually are psychic? Explain. (2 pts.)
2. A professor from Winona State University conducted a survey of n = 200 students to explore computer preference of Winona State undergraduate students (age 18 – 24). The professor believes that a majority of current WSU students prefer the Mac.
a. Define the population of interest. (1 pt)
b. Define the sample. (1 pt)
c. Identify the variable of interest. (1 pt)
d. Recall that the professor’s objective was to determine if a majority of WSU students prefer the Mac over the PC. Write the null and alternative/research hypotheses. (2 pts)
Ho:
Ha:
e. Is this an upper-tail or lower-tail test? Explain. (2 pts.)
f. Suppose in the survey taken by 200 randomly selected students, and 119 of the students surveyed reported that they preferred using a Mac. Do these survey results provide evidence that a majority of WSU students prefer the Mac laptop? Explain.
(3 pts)
3. It has been estimated that in western countries between 10% and 15% of people are left-handed. There have been a number of theories about what causes left-handedness. One theory is that “birth stress”, including birth conditions such a breech births, prolonged labor, premature and cesarean births, tends to push infants towards left-handedness. According to a 1991 New Zealand Herald article, researchers at Queen’s University, Belfast, have investigated this theory by looking at babies in the womb using ultrasound. Of 224 fetuses, 12 sucked their left thumbs while the rest favored their right thumbs.
a. Explain why this is a binomial experiment by checking the required conditions. (2 pts.)
b. The researchers believe that less than 10% of fetuses are left-handed. Set up the appropriate null and alternative/research hypotheses. (2 pts.)
Ho:
Ha:
c. Is this an upper-tail or lower-tail test? Explain. (2 pts.)
d. Do the results provide evidence to support the researcher’s hypothesis? Explain. (3 pts.)
4. Can people sense being stared at? Researcher Rupert Sheldrake believes so. His research has recently been discussed on the television show “Through the Wormhole” which is narrated by Morgan Freeman. Rupert Sheldrake believes in something called the morphic field and morphic resonance that leads to different extra-sensory abilities such as the ability to sense being stared at. He has studied this phenomenon through years of experimentation. In one of his experiments results were obtained from 800 trials using 40 subjects (each subject was tested 20 times). In each trial the blindfolded subject has to state whether or not they were being stared at. Each subject was stared at in 10 of the trials and not stared in the other 10 in a random order. In the 800 trials the subjects correctly identified the staring status 441 times.
You can read more about Dr. Sheldrake’s research in a paper linked under Add’l Links.
a. Explain why this is a binomial experiment by checking the required conditions.
(2 pts.)
b. Set up the appropriate null and alternative/research hypotheses or Dr. Sheldrake’s staring experiments? (2 pts.)
Ho:
Ha:
c. Is this an upper-tail or lower-tail test? Explain. (2 pts.)
d. Do the results provide evidence to support of Dr. Sheldrake’s theory that people can sense being stared at? Explain. (3 pts.)
5. The effect of a social competence training course is tested. 15 Subjects are tested before and after training for social competence on a measured on a seven point Likert scale, high scores the higher the level of social competence. Thus the response is ordinal.
Subject / BeforeTraining / After
Training / Difference =
After - Before / Sign of
Difference
1 / 5 / 6 / 1
2 / 3 / 2 / -1
3 / 4 / 4 / 0
4 / 2 / 4 / 2
5 / 1 / 3 / 2
6 / 6 / 6 / 0
7 / 7 / 7 / 0
8 / 3 / 5 / 2
9 / 2 / 3 / 1
10 / 3 / 5 / 2
11 / 5 / 5 / 0
12 / 1 / 3 / 2
13 / 4 / 4 / 0
14 / 4 / 5 / 1
15 / 3 / 2 / -1
a. When considering the sign of the difference (+, -, or 0) which of these indicates that the subject’s social competence improved after training? Explain. (2 pts.)
b. If the training program in reality does nothing to improve a person’s social competence score, what is the probability their score will go up? Go down?
Explain. (2 pts.)
c. After throwing out the subjects whose scores did not change, do we have evidence that in the general the training program tends to improve the social competence score of participants? Explain using a binomial probability to justify your answer.. (3 pts.)
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