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:
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:
Class 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?
5. What percent of the participants are married (RELAT)?
6. What is the modal level of relationship happiness (HAPPY)?
7. What is the median income of the participants’ partners (INC2)?
8. What percent of the participants are age 51 or older?
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 onesample t test or a twoindependentsample t test.
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 onesample ttest. How would you report the results?
5. What is the mean and standard deviation for the Lifestyle score (L)?
6. The first case shown in the data file is a firefighter with a financial RiskTaking score (R) of 38. What is his RiskTaking zscore (hint: you will need to find the RiskTaking mean and standard deviation)?
7. Perform independent sample ttests on the Lifestyle, Dependency, and RiskTaking scores (L, D, and R) comparing men and women (GENDER1). Use p < .05 as your alpha level and apply a twotailed test. On each of the three scales, do men or women have a significantly higher score?
8. The median US salary is $50,700, according to US Census data. Using a onesample ttest, test to see if participant income (INC1) is different from the national average. Use a twotailed test and an alpha level of 5%.
Statistics Exercise III: Relatedsample 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 onesample, twoindependentsample, or relatedsamples t test is most appropriate. If it is a relatedsamples t test, indicate whether the test is a repeatedmeasures design or a matchedpairs design.
2.
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 pairedsample ttest and an alpha level of 1%. How would you interpret the results of this test?
4. What is the 95% confidence interval for the difference between participant and partner age?
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?
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 oneway ANOVA to look at whether income (INC1) differs by type of relationship (RELAT). Which of the following describes your result:
Perform a 2way 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:
4. The main effect due to marital status indicates:
5. The interaction effect indicates:
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.
3. Which is the predictor variable (X) and which is the criterion variable (Y) for each of the following examples?
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?
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?
6. What is the Pearson r correlation between participants’ ages and the age of their partners (AGE1, AGE2)?
7. Look at the correlation between RiskTaking (R) and Relationship Happiness (HAPPY). Use the standard alpha level of 5%. How would you describe the relationship?
8. If you randomly chose someone from this sample, what is the chance that they described their relationship as either Happy or Very Happy?
Statistics Exercise VI: Nonparametric 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 chisquare statistic is 5.143. The pvalue 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.
2. The calculator at this link will allow you to perform a oneway chisquare 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 chisquare, degrees of freedom, pvalue 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 nonparametric statistical tests with their parametric counterpart by putting the corresponding letter on the line.
Friedman test
KruskalWallis H test
MannWhitney U test
Wilcoxon SignedRanks T test
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 chisquare 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:
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 chisquare 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?
6. Looking at the results of your chisquare test and the associated crosstabs table, what percentage of college graduates report that they are financially comfortable?
7. What is the phicoefficient for the relationship between college graduation and financial comfort?
8. Now look at the relationship between marital status (MSTAT) and college graduation using a chisquare test. What would you conclude?
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