The purpose of the assignment is to provide an exercise on how to conduct one statistical material with appropriate tables and charts from a statistical package, here SPSS, and report the result in a written report.
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Assignments must be written in a group with at most three students. The deadline for the report is 31 March, 7 days after the written exam. The reports should be specified with the group member’s names and front numbers.
Grade: Passed, failed (completion possible).
Report the results in a report. Outline Proposal:
• Start the report with a title page containing the title, name and personal identification number.
• The text itself should consist of
– Short introduction
– Presentation of the material and income statement. For each printout (table, chart) of relevance, there should be some form of comment or discussion. All figures and tables should be indexed and referenced in the text.
– Short summary.
Crosstable.
In order to improve the customer’s satisfaction level, a company sends out a survey of 582 customers from four different chain stores. From the survey, it turns out the quality of customer service is an important factor that affects the customer’s satisfaction. The information of the survey is given in the data set “satisf.sav”. The variable “Store” represents the different stores and the variable “overall” represents the customer’s satisfaction levels. Test if the different store gives different customer satisfaction level under the 5% significant level. What is your conclusion?
Tips: Analyze – Descriptive Statistics – Crosstabs;
Row: store, Column: overall;
Statistics: choose the option Chi-square;
Cells: under Percentages: choose Row, Column.
Simple linear regression
A factory keeps records of the number of working shifts each month and the output. On an intuitive basis, it is believed that the number of working shifts is an important determinant of output. Data is available in the workingoutput.sav file. One may wonder how strong such a relation may be, and if it is even significant.
Consider the following model:
Where x is the amount of working shifts and y is the output.
a. calculate the correlation coefficient (Pearson’s correlation coefficient) between variables X and Y. Is the relation strong? Is the correlation significantly different from zero? Test the hypotheses on level.
b. What is the interpretation of the intercept in this specific model? Test the hypothesis vs. at level.
c. Test the hypothesis versus at level. Comment the conclusion of the test. Is it in line with what you expected?
Tips:
Correlation coefficient: Analyze – Correlate – Bivariate;
Variables: shifts_worked and Output.
Correlation Coefficients: Pearson.
Linear regression and hypothesis testing:
Analyze – regression – Linear;
dependent variable: Output; independent: shifts_worked.
Multiple linear regression
Several countries in EU have the problem of budget deficit during the last 20 – 30 years. So some researches are conducted in order to formulate a connection between the deficit and some macroeconomic factors. Economic theory shows that the connection can be described by a multiple linear regression as follows:
where Y is budget, X1 is gdp (gdp), X2 is interest rates (rate); X3 is the price level (price), X4 is gross government debt (debt) och X5 is the unemployment rates (unempl). are parameters should be estimated by SPSS and is the error term. File “UK budget.sav” contains the information with regards to the UK budget. Use the dataset to answer the following questions:
- Testa hypotheses vs alternative hypothesis: there is at least one parameter that doesn’t equal to 0 under the significant level 5%. What is your conclusion? (F-test in ANOVA table)
- Test if the unemployment rates have a significant effect on the budget deficit (this is equivalent to test the statistical significantly different from 0). What is your conclusion?
Tips: Analyse – regression – Linear;
dependent variable: budget; independent: gdp; rate; price; debt and unempl.
Wilcoxon signed-rank test
One analyst in a finance company would like to investigate the changes in the yearly returns before and after an economic shock. It is known that the data is non-normally but symmetrically distributed. Thus, a Wilcoxon singed-rank test is used for this case. The data material is collected in the file ”mutualfund.sav”. Test if the median return is the same before and after the economic shock by running a hypothesis test under 5% significant level. What is your conclusion?
Tips: Analyze – Nonparametric Tests – Related samples;
Objective: Customize analysis;
Fields – Test fields: Return_before, Return_after;
Settings – Customize tests: Wilcoxon matched-pair signed-rank.