10.4.36 Determine the upper-tail critical values of F in each of the following two-tail tests.
a. alphaequals0.05, n1equals25, n2equals16 .
b. alphaequals0.02, n1equals25, n2equals16 .
c. alphaequals0.10, n1equals25, n2equals16
(Round to two decimal places as needed.)
In: Math
A) Assume that 12 jurors are randomly selected from a population in which 87% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities.
xx | P(x)P(x) |
---|---|
0 | 0+ |
1 | 0+ |
2 | 0+ |
3 | 0+ |
4 | 0+ |
5 | 0.0002 |
6 | 0.0019 |
7 | 0.0111 |
8 | 0.0464 |
9 | 0.138 |
10 | 0.2771 |
11 | 0.3372 |
12 | 0.188 |
Find the probability of exactly 5 Mexican-Americans among 12
jurors.
P(x=5)=P(x=5)=
Find the probability of 5 or fewer Mexican-Americans among 12
jurors.
P(x≤5)=P(x≤5)=
Does 5 Mexican-Americans among 12 jurors suggest that the selection
process discriminates against Mexican-Americans?
yes?
no?
B) A company prices its tornado insurance using the following
assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.12.
• The number of tornadoes in any calendar year is independent of
the number of tornados in any other calendar year.
Using the company's assumptions, calculate the probability that
there are fewer than 4 tornadoes in a 14-year period.
In: Math
Practice Problems (Chapters 7 and 8)
Chapter 7
1. Which would you expect to be more variable: (a) the distribution of scores in a population or (b) the distribution of sample means based on random samples of 25 cases from this population. Explain.
Chapter 8
8. What is meant by statistical significance? Why does your author suggest that it may not always be adequate for purposes of research?
9. Provide an example of the following: (a) A research problem appropriate for a non-directional test using the one-sample z-statistic. (b) A research problem appropriate for a directional test using the one-sample t-statistic.
10. Consider the data in problem 11 in the text (page 199). Enter these data into SPSS and conduct a test of the null hypothesis.
In: Math
Practice Problems (Chapters 9 and 11)
Chapter 9
1. Given a sample mean of 12.5 based on 25 cases and a population variance of 10, construct a 95% confidence interval for the population mean. Interpret the resulting interval.
2. What can be expected to happen to the length of a confidence interval as the size of the sample used to construct it increases. Explain.
3. In a short paragraph, explain the logic of confidence intervals.
4. Can confidence intervals be used to test hypotheses? Explain.
Chapter 11
5. Describe a research study appropriate for an independent measures t-test.
6. Describe a research study appropriate for a dependent samples t-test.
7. Consider the data in problem 4 in Chapter 11 (p. 273). Enter these data into SPSS and conduct a test of the null hypothesis. Compute a measure of effect size and construct a 95% confidence interval for your study.
8. Consider the data in problem 5 in Chapter 11 (p. 273). Enter these data into SPSS and conduct a test of the null hypothesis. Compute a measure of effect size and construct a 95% confidence interval for your study.
In: Math
How much "error" is too much before you are no longer confident about your estimates or research findings? Do sampling methods have anything to do with this? Discuss.
In: Math
The following relative frequency distribution was constructed
from a population of 650. Calculate the population mean, the
population variance, and the population standard
deviation.
Class | Relative Frequency |
−20 up to −10 | 0.30 |
−10 up to 0 | 0.20 |
0 up to 10 | 0.40 |
10 up to 20 | 0.10 |
Population Mean -
Population Variance -
Population Standard Deviation -
In: Math
Define each and provide an example.
-1 Convenience Sample
-2 Cross-sectional research design
-3 Research Ethics
-4 Randomization “ Data Collection”
In: Math
You have colleagues who reside in different zip codes. Which measure(s) of central tendency or other descriptive statistics would you use to describe this information? (please answer in full paragraphs - thank you)
In: Math
A recent debate about where in the United States skiers believe
the skiing is best prompted the following survey. Using α = 0.10,
test to see if the best ski area is independent of the level of the
skier. Write the hypotheses, calculate the expected counts, check
the condition, calculate the test statistic, and use either the
critical value approach or the p-value approach to make a
conclusion.
Level of the Skier
U.S. Ski Area Beginner Intermediate Advanced
Tahoe 20 30 40
Utah 10 30 60
Colorado 10 40 50
In: Math
A researcher was interested in the effects of alcohol on attractiveness of mate selected (referred to as the beer goggle effect). She compared the rating (by independent raters) on level of attractiveness of the partners that young people chose at a party. She compared a group before using alcohol then after using alcohol. Assessment was whether their chosen partners differed in levels of attractiveness. Higher scores indicated more attractive partners. The attractiveness of partner for each participant (measured by independent raters) in 2 scenarios for the same group (before using alcohol and after using alcohol) was as follows:
Before using alcohol |
After using alcohol |
5 |
10 |
12 |
14 |
7 |
15 |
5 |
9 |
8 |
11 |
6 |
10 |
10 |
13 |
8 |
11 |
7 |
9 |
In: Math
Think of a problem that you may be interested in that deals with a comparison of two population means. Propose either a confidence interval or a hypothesis test question that compares these two means. Gather appropriate data and post your problem (without a solution) in the discussion topic. Later, respond to your own post with the solution for others to check their work.
For example, you may want to know if the average weight of a rippled potato chip is the same as the average weight of a non-rippled potato chip. You may weigh rippled regular potato chips from a large bag and find weights of 1.7, 1.9, 2.4, 1.3, 1.7, and 2.0 grams. You may weigh non-rippled potato chips from another large bag and find weights of 1.8, 1.6, 1.9, 1.9, and 1.4 grams. Assume a random sample was drawn.
In: Math
The evidence supporting obesity as a risk factor for colon cancer remains inconclusive, especially among women. A study reported the association between obesity (measured at baseline) and colon cancer morbidity as determined from review of medical records and death certificates in a nationally representative cohort of men and women age 25-74 years who participated in the First National Health and Nutrition Examination Survey from 1971 to 1975 and were subsequently followed up through 1992. The following table is from this study for men and women combined.
Baseline body mass index (kg/height)2 |
Number of incident cases of colon cancer |
Person-years of follow up |
Crude incidence rate/100,000 PY |
<22 |
29 |
54,475 |
|
22-<24 |
42 |
39,919 |
|
24-<26 |
37 |
37,610 |
|
26-<28 |
41 |
33,635 |
|
28-<30 |
36 |
22,122 |
|
30+ |
43 |
35,904 |
a. Which of the following best describes the research design used in this study? Choose the ONE best answer. (1 point)
b. Complete the table above by calculating the crude body mass index-specific incidence rates. (Show your work in the table above.) (3 points – ½ point for each correct answer)
c. Calculate the relative risk (rate ratio) of colon cancer associated with a BMI of 30+. Use the lowest BMI category as the reference group. In one sentence interpret your answer. (2 points)
d. Calculate the attributable fraction among those in the 30+ BMI category. In one sentence interpret your answer. (The attributable fraction formulas provided in class can be used even though the data provided here is for rates.) (2 points)
In: Math
Outline the best clustering method for the following tasks (and briefly describe the reason you would make such a design) :
(a) Finding oil spills along a coast line.
(b) Clustering employees in a company based on their salaries and years of working experience.
In: Math
There is a strong linkage between statistical data analysis and data mining. Some people think of data mining as automated and scalable methods for statistical data analysis. Do you agree or disagree with this perception? Present one statistical analysis method that can be automated and/or scaled up nicely by integration with current data mining methodology.
In: Math
You are a news vendor selling the FTU Daily Times every morning. Before you get to work, you go to the printer and buy the day’s paper for $0.35 a copy. You sell a copy of the Sun Times for $1.20. Daily demand is distributed normally with mean = 300 and standard deviation = 75. At the end of each morning, any leftover copies are worthless and they go to a recycle bin. How many copies of the FTU Times should you buy each morning? Based on part (a), what is the probability that you will run out of stock?
In: Math