1. The following table illustrates the BMI for a number of patients recently enrolled in a study investigating the relationship between BMI and type 2 diabetes.
Participant
BMI (kg/m2)
A
26.5
B
19.2
C
29.7
D
27.4
E
30.2
F
28.9
A) Assuming the participants can be considered to be normally distributed, and that they come from a population with a σ=2.4 kg/m2, calculate a 95% confidence interval for the mean BMI of the population for which they represent.
B) Correctly interpret the confidence interval you found above.
2.
Suppose the following table illustrates the ages for a number of participants projected to enroll into a clinical trial looking at early onset of dementia.
Patient
Age
A
64
B
57
C
58
D
53
E
71
F
54
G
63
A) Assuming that these participants can be considered to be normally distributed, and that they come from a population with a σ=4.3 years, calculate a 99% confidence interval for the mean age of the population for which they represent.
B) With the same assumptions listed above, calculate a 90% confidence interval for the mean age of the population for which they represent.
C) Compare the precision of the two confidence intervals.
3.
A new vitamin supplementation program is intended to decrease average resting heart rate in individuals at risk for hypertension. Assume that a team of researchers are hopeful that resting heart rate in their population will get down to less than 68 bpm, in a population with a standard deviation of 2 bpm. In order to test this goal reduction, the team gathers a SRS of 273 participants in their program and calculates a sample average resting heart rate of 74 bpm.
A) Carry out a one sample Z test to determine if the team can conclude that the supplementation program is successful in meeting their goal reduction in resting heart rate. Use an α=0.05.
B) Construct a 95% Confidence interval about the sample mean, and interpret the result.
4.
A consulting company is hired to investigate the relationship between average physician annual income and number of beds present at a local hospital. Assume the following table represents a SRS of hospitals.
Average Physician Annual Income($/year, X)
Number of Beds (Count, Y)
127,655
698
176,526
943
134,253
713
114,534
578
A) Calculate basic descriptive statistics for your X and Y variables.
B) Calculate a correlation coefficient, and interpret your result with respect to strength and direction.
C) Calculate and correctly interpret your r2 for the data.
5.
Assume that the following table of observations in a dataset represents a sample of physician incomes from a hospital. Create a box-plot for the data.
Physician
Income ($1000/year)
Physician
Income ($1000/year)
A
121
G
176
B
124
H
138
C
173
I
169
D
175
J
158
E
186
K
163
F
143
L
154
6.
Two oldsters were sitting on a park bench talking about the old days. The golfer bragged that he had a 76 average when he was in his prime. The bowler snorted and said that his league average was 210 when he was in his prime. What additional information would you need to determine who was the better of the two?
7.
Suppose a small group of expert physicists and mathematicians held a joint conference. You, being an opportunistic sort, talked them all into taking two personality tests. The first test measured the need for achievement (N-Ach) and the second measured the need for affiliation (N-Aff), which is a desire for association with other people. Below are the scores. What conclusions can you reach about the relationship between need for achievement and need for affiliation among these scientists?
Person X Y
N-Ach N-Aff
1 28 12
2 27 10
3 25 14
4 24 18
5 24 11
6 23 15
7 23 16
8 23 19
9 22 22
10 21 20
11 19 18
12 18 24
13 17 25
14 15 23
15 13 26
8.
According to Obi-Wan Kenobe, the last of the Jedi Knights, “The Force can have an influence on the weak-minded.” Unfortunately for psychology, concepts like a weak mind have been abandoned and therefore psychologists cannot hope to understand this most important intervening variable. Please answer the following question which you will have no difficulty with; which you will answer quickly, completely, and correctly. The beautiful Princess Leia, in a prescience trance, saw a funny hair style on 1920s movie stars in America. She decided to adopt this hair style and practiced and practiced winding her hair in circles using her ears as cores. On the average she got 12 coils and the standard deviation was two coils. What is the probability that, on the day she was rescued by Luke, Han, and Chewey, she had between 11 and 14 coils?
9.
A counselor at the local chapter of Impulse Buyers Anonymous had just conducted a weekend workshop on how to be less suggestible. To find out if the workshop had any effect, she had each participant fill out a questionnaire that measured suggestibility, with high scores indicating high suggestibility. (Several such questionnaires exist.) Suppose that the national norm (mean) for the questionnaire that was used was 25 and that the participants produced the following statistics. Construct a 95 percent confidence interval and write a sentence of interpretation that tells about the effect of the workshop.
= 242 2 = 5,413 N = 11
10.
Identify each experiment below as an independent samples design or a paired samples design.
a. At a hunting club the squirrel hunters had a contest with the quail hunters to see who could hit the most moving targets.
b. A consumer-testing group compared Boraxo and Tide to determine which got stuff whiter. Sheets that had been placed for 12 hours in a bathtub of mud were washed and the amount of light reflected was measured with a photometer.
c. Fifth-grade American Indians were matched as a group to a group of New York Puerto Ricans on SES, IQ, and reading level. They were then given a questionnaire on attitudes toward school.
d. On the basis of a pretest on knowledge of foreign governments, each student in the 9:00 class was matched with a student in the 10:30 class. The 9:00 class used a “participant approach” to the study of politics and the 10:30 class used the “Heidleburg method.” At the end of the term the same test was given to both classes.
11.
Cowboys from the mythical Stats Bar-X Ranch competed in a singing contest at the Dry Gulch Saloon where they sang against cowpokes from the Dragging y Ranch. The songs were psychowestern (which are like psychedelic songs, but with a twangy ranch dressing). A Stats Bar-X researcher counted the number of people clapping after each song over the hour of the contest, during which the two groups alternated singing.
a. Compare the two groups with a t test, find the effect size index, and write an interpretation of what you find.
b. Find the 95 percent confidence interval about the mean difference and write an interpretation.
Stats Bar-X Dragging y
12:00 set 21 23
12:10 set 25 18
12:20 set 20 16
12:30 set 17 14
12:40 set 14 10
12:50 set 8 3
