Statistics Assignment Question Exercise
Statistics Exercise I: Descriptive statistics
These weekly exercises provide the opportunity for you to understand and apply statistical methods and analysis.
1. Given the following values of the mean and median, state the likely shape of the distribution:
- mean = 4, median = 4
- mean = 12, median = 2
- mean = 8, median = 18
- mean = 6, median = 14
- mean = 10, median = 3
- mean = 8, median = 8
2. IQ scores have a mean of 100 and a standard deviation of 15. What percentile corresponds to an IQ score of 115? Explain the steps you took to find the percentile.
3. Which measure of central tendency would you use for the following variables (mean, median or mode). Explain your choice.
Gender:
className rank at a college:
Age of high school students:
A skewed income distribution (90% with incomes under $150K; a few with incomes of several million):
Use SPSS and the data file found in syllabus resources (DATA540.SAV) to answer the following questions. Round your answers to the nearest dollar, percentage point, or whole number.
4. What is the mean annual income (INC1) of the participants?
- $43,282
- $72,133
- $47,113
- $34,282
5. What percent of the participants are married (RELAT)?
- 28%
- 33%
- 51%
- 59%
6. What is the modal level of relationship happiness (HAPPY)?
- Mixed
- Happy
- Very Happy
- Cannot be determined
7. What is the median income of the participants’ partners (INC2)?
- $24,212
- $28,945
- $32,000
- $48,975
8. What percent of the participants are age 51 or older?
- 4%
- 5%
- 7%
- 10%
Statistics Exercise II: Statistical inference, 1- and 2-sample t-tests
These weekly exercises provide the opportunity for you to understand and apply statistical methods and analysis. Unless otherwise stated, use 5% (.05) as your alpha level (cutoff for statistical significance).
1. Define "power" in relation to hypothesis testing.
2. Alpha (a) is used to measure the error for decisions concerning true null hypotheses. What is beta (ß) error used to measure?
3. In the following studies, state whether you would use a one-sample t test or a two-independent-sample t test.
- A study testing whether night-shift workers sleep the recommended 8 hours per day
- A study measuring differences in attitudes about morality among Democrats and Republicans
- An experiment measuring differences in brain activity among rats placed on either a continuous or an intermittent reward schedule
Use SPSS and the data file found in syllabus resources (DATA540.SAV) to answer the following questions. Round your answers to the nearest dollar, percentage point, or whole number.
4. Test the age of the participants (AGE1) against the null hypothesis H_{0 }= 34. Use a one-sample t-test. How would you report the results?
- t = -1.862, df = 399, p > .05
- t = -1.862, df = 399, p < .05
- t = 1.645, df = 399, p > .05
- t = 1.645, df = 399, p < .05
5. What is the mean and standard deviation for the Lifestyle score (L)?
- 31.22, 7.99
- 36.19, 8.54
- 30.03, 7.28
- 55, 13
6. The first case shown in the data file is a firefighter with a financial Risk-Taking score (R) of 38. What is his Risk-Taking z-score (hint: you will need to find the Risk-Taking mean and standard deviation)?
- 0.179
- -0.223
- 1.342
- -1.223
7. Perform independent sample t-tests on the Lifestyle, Dependency, and Risk-Taking scores (L, D, and R) comparing men and women (GENDER1). Use p < .05 as your alpha level and apply a two-tailed test. On each of the three scales, do men or women have a significantly higher score?
- Lifestyle: Men, Dependency: Women, Risk-Taking: Men.
- Lifestyle: Not significantly different, Dependency: Women, Risk-Taking: Men
- Lifestyle: Women, Dependency: Women, Risk-Taking: Men
- Lifestyle: Men, Dependency: Men, Risk-Taking: Not significantly different
8. The median US salary is $50,700, according to US Census data. Using a one-sample t-test, test to see if participant income (INC1) is different from the national average. Use a two-tailed test and an alpha level of 5%.
- Participant income is significantly greater than the national average
- Participant income is significantly less than the national average
- Participant income is not significantly different from the national average
- Participant income cannot be compared to the national average
Statistics Exercise III: Related-sample t; confidence intervals
Statistics Exercise III: Related-sample t; confidence intervals
These weekly exercises provide the opportunity for you to understand and apply statistical methods and analysis. Unless otherwise stated, use 5% (.05) as your alpha level (cutoff for statistical significance).
1. For each example, state whether the one-sample, two-independent-sample, or related-samples t test is most appropriate. If it is a related-samples t test, indicate whether the test is a repeated-measures design or a matched-pairs design.
- A professor tests whether students sitting in the front row score higher on an exam than students sitting in the back row.
- A graduate student selects a sample of 25 participants to test whether the average time students attend to a task is greater than 30 minutes.
- A researcher matches right-handed and left-handed siblings to test whether right-handed siblings express greater emotional intelligence than left-handed siblings.
- A principal at a local school wants to know how much students gain from being in an honors className. He gives students in an honors English className a test prior to the school year and again at the end of the school year to measure how much students learned during the year.
2.
- A random sample of 25 professional basketball players shows a mean height of 6 feet, 5 inches with a 95% confidence interval of 0.4 inches. Explain what this indicates.
- If the sample were smaller, would the confidence interval become smaller or larger? Explain.
- If you wanted a higher level of confidence (99%) would the confidence interval become smaller or larger? Explain.
Use SPSS and the data file found in syllabus resources (DATA540.SAV) to answer the following questions. Round your answers to the nearest dollar, percentage point, or whole number.
3. Test to see if there is a significant difference between the age of the participant and the age of the partner. Use a paired-sample t-test and an alpha level of 1%. How would you interpret the results of this test?
- The partners are significantly older than the participants.
- The partners are significantly younger than the participants.
- The age of the participants and partners are not significantly different.
- Sometimes the partners are older, sometimes the participants are older.
4. What is the 95% confidence interval for the difference between participant and partner age?
- The partner is from .60 to 1.76 years older than the participant
- The participant is from .60 to 1.76 years older than the partner
- The partner is from 5.88 to 9.45 years older than the participant
- The participant is from 5.88 to 9.45 years older than the partner
Statistics Exercise IV: Analysis of Variance
Statistics Exercise IV: Analysis of Variance
These weekly exercises provide the opportunity for you to understand and apply statistical methods and analysis. Unless otherwise stated, use 5% (.05) as your alpha level (cutoff for statistical significance).
1. Which type of ANOVA would you use for each of the studies below?
- One-way between subjects (independent groups)
- One-way within subjects (repeated measures)
- Two-way between subjects
- Measure the self-esteem of the same group of college students at the beginning, middle and end of their freshman year.
- Compare math skills for three different professional groups: physicians, attorneys and psychologists.
- Measure Body Mass Index (BMI) for persons who take Supplement X vs. a placebo and who either exercise regularly or don’t. So there are four groups: 1) Exercise/Take Supplement X, 2) Don’t Exercise/Take Supplement X, 3) Exercise/Take Placebo, 4) Don’t Exercise/Take Placebo
- Look at satisfaction with mental health services based on the client’s ethnicity (White, Black, Hispanic, Asian or Other) and how they were greeted on their initial visit (receptionist smiles or does not smile).
Use SPSS and the data file found in syllabus resources (DATA540.SAV) to answer the following questions. Round your answers to the nearest dollar, percentage point, or whole number.
2. Perform a one-way ANOVA to look at whether income (INC1) differs by type of relationship (RELAT). Which of the following describes your result:
- F(3,396) = 4.91, p > .05
- F(3,396) = 4.91, p < .001
- F(3,396) = 6.85, p > .05
- F(3,396) = 6.85, p < .001
Perform a 2-way ANOVA with participant’s income (INC1) as the dependent variable and with gender (GENDER1) and marital status (MSTAT) as independent variables. Interpret your results in questions 6, 7 and 8. (Hint: click the “Plots” button in the Univariate routine to create a graph).
3. The main effect due to gender indicates that:
- Women earn more than men.
- Men earn more than women.
- Men and women have incomes that are not significantly different.
- Participants earn more than their partners.
4. The main effect due to marital status indicates:
- Your income tends to decrease after a divorce.
- Getting married tends to increase your income.
- Marital status is unrelated to income.
- Married people tend to earn more than single people.
5. The interaction effect indicates:
- Men earn more than women and married people earn more than singles.
- The male/female income difference is greater when comparing married people than when comparing singles.
- The interaction effect is non-significant.
- Marriage helps men’s careers more than it helps women’s careers.
Statistics Exercise V: Correlation and Regression
Statistics Exercise V: Correlation and Regression
These weekly exercises provide the opportunity for you to understand and apply statistical methods and analysis. Unless otherwise stated, use 5% (.05) as your alpha level (cutoff for statistical significance).
1. What information does a correlation coefficient convey?
2. State whether each of the following is an example of a positive correlation or a negative correlation.
- Higher education level is associated with a larger annual income.
- Increased testosterone is associated with increased aggression.
- The smaller the className size, the more students believe they are receiving a quality education.
- Rising prices of apples are associated with the sale of fewer apples.
3. Which is the predictor variable (X) and which is the criterion variable (Y) for each of the following examples?
- A researcher tests whether the size of an audience can predict the number of mistakes a student makes during a classroom presentation.
- A military officer tests whether the duration of an overseas tour can predict the morale among troops overseas.
- A social psychologist tests whether the size of a toy in cereal boxes can predict preferences for that cereal.
Use SPSS and the data file found in syllabus resources (DATA540.SAV) to answer the following questions. Round your answers to the nearest dollar, percentage point, or whole number.
4. What is the regression equation that would best predict relationship happiness (HAPPY) from the Lifestyle (L) score?
- HAPPY = L - .143
- HAPPY = .23L – 4.5
- HAPPY = .42L + .23
- HAPPY = 4.47 - .018L
5. The Lifestyle score (L) measures the degree to which a participant desires a luxurious lifestyle. The Dependency score (D) measures the degree to which a participant expects others to provide financial support. Compute the correlation between these two variables. Which of the statements below best describes the relationship?
- People who want a more frugal lifestyle tend to be more financially dependent.
- People who want a more luxurious lifestyle tend to be more financially dependent.
- People who want a more luxurious lifestyle tend to be less financially dependent.
- There is no relationship between desired lifestyle and financial dependency.
6. What is the Pearson r correlation between participants’ ages and the age of their partners (AGE1, AGE2)?
- .000
- .413
- .622
- .822
7. Look at the correlation between Risk-Taking (R) and Relationship Happiness (HAPPY). Use the standard alpha level of 5%. How would you describe the relationship?
- The relationship is non-significant.
- There is a significant negative relationship.
- There is a significant positive relationship.
- The correlation is zero.
8. If you randomly chose someone from this sample, what is the chance that they described their relationship as either Happy or Very Happy?
- 32%
- 37%
- 56%
- 69%
Statistics Exercise VI: Non-parametric statistics
Statistics Exercise VI: Non-parametric statistics
These weekly exercises provide the opportunity for you to understand and apply statistical methods and analysis. Unless otherwise stated, use 5% (.05) as your alpha level (cutoff for statistical significance).
Ice Cream Flavor Preference by Gender | |||
Men |
Women |
Marginal Row Totals | |
Vanilla |
15 |
10 |
25 |
Chocolate |
30 |
5 |
35 |
Marginal Column Totals |
45 |
15 |
60 (Grand Total) |
The chi-square statistic is 5.143. The p-value is .0233. This result is significant at p < .05.
1. The chart above shows male and female preferences for vanilla vs. chocolate ice cream among men and women.
- What percent of men prefer chocolate over vanilla?
- What percent of women prefer chocolate over vanilla?
- Report the results of the statistical test in plain language:
2. The calculator at this link will allow you to perform a one-way chi-square or “goodness of fit test”:
http://vassarstats.net/csfit.html
Fifty students can choose between four different professors to take Introductory Statistics. The number choosing each professor is shown below. Use the calculator above to test the null hypothesis that there is no preference for professors -- that there is an equal chance of choosing each of them. Report your results including chi-square, degrees of freedom, p-value and your interpretation. Use an alpha level of .05. Be careful not to over interpret – state only what the test result tells you.
Professor |
N |
Dr. Able |
20 |
Dr. Baker |
8 |
Dr. Chavez |
14 |
Dr. Davis |
8 |
3. Match these non-parametric statistical tests with their parametric counterpart by putting the corresponding letter on the line.
Friedman test
Kruskal-Wallis H test
Mann-Whitney U test
Wilcoxon Signed-Ranks T test
- Paired-sample t-test
- Independent-sample t-test
- One-way ANOVA, independent samples
- One-way ANOVA, repeated measures
Use SPSS and the data file found in syllabus resources (DATA540.SAV) to answer the following questions. Round your answers to the nearest dollar, percentage point, or whole number.
4. Perform a chi-square test to look at the relationship between region of the country (REGION) and financial comfort (FCOMFORT). Using alpha = .05, what would you conclude from your test:
- Financial comfort differs depending on the area one lives in.
- People living in less expensive areas are more likely to report that they are financially comfortable.
- There is not a significant relationship between region and financial comfort.
- People living in the northeast region are most likely to report that they are financially struggling.
Click TRANSFORM --> COMPUTE VARIABLE. Type COLLEGE in the "Target Variable" box and type EDUC1 GE 4 in the "Numeric Expression" box. Then click “OK.” This will create a new variable, COLLEGE, that is "1" for college graduates and "0" for those with less education.
5. Perform a chi-square test to look at the relationship between college graduation (COLLEGE) and financial comfort (FCOMFORT). Notice how FCOMFORT is coded, 1=Comfortable, 2=Struggling. Using alpha = .05, what would you conclude from your test?
- College graduates are more likely to be financially comfortable than non-graduates
- College graduates are less likely to be financially comfortable than non-graduates
- There is not a significant difference between college graduates and non-graduates with regard to financial comfort
- Graduating college will generally increase your income
6. Looking at the results of your chi-square test and the associated crosstabs table, what percentage of college graduates report that they are financially comfortable?
- 41%
- 47%
- 53%
- 59%
7. What is the phi-coefficient for the relationship between college graduation and financial comfort?
- -.470
- -.331
- -.255
- -.118
8. Now look at the relationship between marital status (MSTAT) and college graduation using a chi-square test. What would you conclude?
- Married people are more often college graduates than singles
- College graduates are more often married than non-graduates
- There is not a significant relationship between marital status and college graduation
- Both “a” and “b” are true