Levels of measurement, sampling methods, and statistical analysis
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.
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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.
6.44X10-5
12. In a study of families with children with disabilities, groups of 6 U.S. households were randomly selected. In the table below, the random variable x represents the number of households among 6 that had a child with a disability living there.
x
P (x)
0
0.539
1
0.351
2
0.095
3
0.014
4
0.001
5
0+
6
0+
a. What is the mean? .14286
b. What is the standard deviation? .21606
c. Is this a probability distribution? Why or why not? No, not enough info.
13. A dental company my son works for makes implants so accurately that there is a 1/2000 probability of getting a defective implant. My dentist ordered 5 implants and claimed 2 of them were defective.
a. Find the probability of getting exactly 2 defective implants when buying 5 implants.
2.5 x 10 -5
b. Find the probability of getting at least 2 defective implants when buying 5 implants.
1
c. Does my dentist's claim of getting 2 defective implants seem valid? Explain. No it is quite unlikely
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