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.

2. Given a normal distribution of scores that has a mean of 50 and a standard deviation of 10, what is the probability of selecting a score that is greater than 65? If a random sample of 10 scores were selected from this population, what is the probability that the mean score for this sample would be greater than 65?

3. In a short paragraph, explain the logic of inferential statistics (The Hinkle et al. text refers to this as the chain of reasoning in inferential statistics).

4. What is the central limit theorem and what role does it play in inferential statistics?

Chapter 8       

5. Describe a study in which a one sample t-test is appropriate. Be sure to state your research question, hypotheses, significance level, critical value, etc.

6. List the steps in the hypothesis testing sequence.

7. In a short paragraph, explain Type I and Type II errors to an audience that has no previous experience with statistics.

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.

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.

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.

The following relative frequency distribution was constructed from a population of 650. Calculate the population mean, the population variance, and the population standard deviation.

Population Mean -

Population Variance -

Population Standard Deviation -

Define each and provide an example.

-1 Convenience Sample

-2 Cross-sectional research design

-3 Research Ethics

-4 Randomization “ Data Collection”

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)

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

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:

1. Test the hypothesis (Use alpha level of 0.05) using both manual and MS Excel calculations that there is no statistically significant difference between alcohol using and non-alcohol using group with regard to the level of attractiveness of the partners they chose by the end of the party. In your answer determine and interpret the strength of this relationship.

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.

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.

a. Which of the following best describes the research design used in this study? Choose the ONE best answer. (1 point)

1. Cross-sectional survey
2. Ecological study
3. Population based case control study
4. Cohort study
5. None of the above

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)

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.

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.

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?

What are the major differences among the three methods for the evaluation of the accuracy of a classifier:

(a) hold-out method,

(b) cross-validation, and

(c) bootstrap?

The publisher of a sports magazine plans to offer new subscribers one of three gifts: a sweatshirt with the logo of their favorite team, a coffee cup with the logo of their favorite team, or a pair of earrings with the logo of their favorite team. In a sample of 500 new subscribers, the number selecting each gift is reported below. At the .05 significance level, is there a preference for the gifts or should we conclude that the gifts are equally well liked?