This is not an essay, rather, the problem deals with answering as set of questions. The questions deal with probabilities and statistics. Topics covered include, standard deviation, sampling sizes, box graphs, determining the validity of a statistical model and various other basic topics dealing with this mathematical science. The questions present a general understanding of the topic.
Ethics
Please make sure to show all work for each problem requiring calculations. Please highlight final answer.
What is the level of measurement for each of the following:
a) Final grades in this class ____Ordinal
b) Weights of newborn babies ____Nominal
c) Seasons of the year ____Interval
d) Boiling temperatures of different liquids ____Ratio
Types of sampling used:
a) I collect data from my class ____Simple
b) Data from every fourth patient in the hospital ____Stratified
c) Data from 400 randomly selected students from those majoring in business, 763 randomly selected students from those majoring in education, and 392 randomly selected students from those majoring in criminal justice. ____Cluster
d) Data from 4230 adults after phone numbers were randomly generated ____Quota
3. The following data were collected on amounts of lawn debris after the major storm this past summer:
Pounds
Frequency
2-5
2
6-9
2
10-13
6
14-17
15
a) What is the class width?
b) What are the class midpoints?
c) What are the class boundaries?
d) Create a histogram
4. The weekly salaries for teachers of different grade levels at my school are as follows:
Do the different grades have much variation in salary? Base your decision on the calculated standard which needs to be part of your solution.
The Standard deviation is 272.733. This is quite a large variation considering the fourth salary is only 431...
5. I counted the number of words on each posting from my Class Announcements and found the following:
What is the 5-number summary?
Minium: 128, Max: 172, Median: 150, Q1:140, Q2:158.5
Construct a boxplot.
6. A study compared cognitive behavioral therapy (CBT) and regular talk therapy for patients with anxiety. It was found that among 73 patients treated with CBT, there was a 92% success rate. Among 83 patients treated with regular talk therapy, there was a 72% success rate. Calculations using these results showed if there really is no different in success rates between CBT and regular talk therapy, then there is about a one chance in 1000 (1/1000) of getting success rates like these.
a) Should we conclude that CBT is better than regular talk therapy for anxiety? No
b) Does the result have statistical significance? Why or why not?
The results lack significance due to the sample size being relatively small.
c) Does the result have practical significance? Why or why not?
These results are more practical due to the fact that there is some established relationship between the therapy and the disorder. It is important however that causality is not established.
d) Should we recommend CBT for treatment of anxiety?
It would depend on who the patient is.
7. My cousin was 38 when she retired from the military. Most people who retire have a mean age of 43.8 years. The standard deviation is 8.9 years.
a) What is the difference between my cousin's age and the mean age?
5 .8 years
b) How many standard deviations is that (difference found in part a)?
1.53 deviations.
c) Convert my cousin's age to a z-score
-.065169
d) If we consider "usual" age to be those that convert to a z score between -2 and +2, is my cousin's age usual or unusual?
Usual...
8. A survey was conducted asking people if they thought they were overweight. Participants were randomly selected. Data were analyzed by how many participants in each age group were male or female.
Age
18 -- 21
22 -- 29
30 -- 39
40 -- 49
50 -- 59
60 +
Female
73
Male
11
20
33
16
27
49
a) What is the probability that the randomly selected participant is someone 60 or over and is female? 202/1205= .1677 =17%
b) I'm not interested in males or in participants under 22 years of age or over 59 years of age. What is the probability that the randomly selected person is someone I'm not interested in?
976/1205= .801= 80%
9. Psychologists frequently measure achievement using a test with scores that are normally distributed, with a mean of 100 and a standard deviation of 15.
a. What is the probability that a child I test has an achievement score >131.5?
.0179
b. What is the probability that a child I test has an achievement score between 110 and 120?
.1613
c. What is the achievement score separating the bottom 37% from the others?
10. A plant in DC manufactures 400 calculators, of which 3 are defective. The Chicago plant of the same company manufactures 800 calculators, of which 2 are defective. If one of the 1200 calculators is randomly selected and is found to be defective, what is the probability that it was manufactured in DC?
66%
11. Twenty students are eligible for a GT/LD program in my school district. A simple random sample of five is selected.
You’re 82% through this paper. Sign up to read the full paper.
Sign Up Now — Instant Access Already a member? Log inAlways verify citation format against your institution’s current style guide requirements.