Winterterm 2006/07 / Prof. Dr. Peter Schmidt
Economics & Statistics
Research Methods
resit - Monday, November 13th 14.00(60minutes = 60 points)
Please note:
- At first please check the exam paper: are there 5pages / all pages well readable?
- Please only work in the exam paper; use the boxes for your answers. You do not need own paper.
- Your calculations should be shown.The complete solution processmust be traceable!
- You can achieve 60 points – in 60 minutes! => one minute is approximately worth onepoint; please consider the indicated scores. The tasks are formulated that way that usually short answers are required. Therefore do not spend too much time with "inferior" tasks!
NEW!: To obtain a 100% marks you have to gather 60 points. There are four tasks worth 20 points each you have to answer only 3 of the four questions! - Permitted material: Pens, ruler, calculator (without word processing functions), “Statistics Formulas” by P. Schmidt, language dictionary English.
- Please do not use a pencil (except in diagrams) nor red pens.
- Mobile Phones have to be switched off !
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Task 1Concepts and Definitions (20 points in total)
Task 1.1Why is a literature review necessary for a proposal?(5 P)
(self explaining)
Task 1.2Briefly describe the terms: “concept” and “variable”(5 P)
Concepts are meanings abstracted from our observations; they classify or categorize objects or events that have common characteristics beyond a single observation (see a). A variable is a concept or construct to which numerals or values are assigned; this operationalization permits the construct or concept to be empirically tested. In informal usage, a variable is often used as a synonym for construct or property being studied.
Task 1.3What problems of secondary data quality must researchers face? How can they deal with them? (5 P)
There are two chief problems. One is the question of accuracy. Every study is done for some reason (purpose, scope, audience, and authority) and we should assure ourselves that the data we use is not biased in such a way that it is unusable. In addition, there is the definition problem. Do we know the operational definitions used in the study? Are they compatible with our own?
Task 1.4What are the basic differences among nominal, ordinal, interval, and ratio scales?(5 P)
Nominal scales differentiate among objects and properties only on the basis of being alike or different from other scale values. The “named” characteristics are presumably mutually exclusive and in an exhaustive set of categories. Ordinal scales incorporate this feature of differentiability plus the concept of order (i.e., a subject may exhibit more, less, or the same amount of a property as another subject). Interval scales incorporate both of the features of the ordinal scale plus the added one of distance between scale points. For example, the distance between 1 and 2 is the same as between 2 and 3. Finally, ratio scales include all of the interval scale features plus the added feature of having a zero origin. This allows us to say that 4 is twice as large as 2 and to multiply scale values.
Task 2Methodological Concepts:(20points in total)
Task 2.1a) Describe the research question hierarchy using the following graph. b) Provide an own realistic example(that also fits for 2.2 and 2.3)(8 P)
-- describe in your own words --
Task 2.2a) Describe the concepts of null hypothesis and alternative hypothesis. b) Develop both hypotheses for you example (from Task 2.1)(7 P)
The null is a hypothesis of no change or no difference. More specifically, we conclude that a population value has not changed from one time to another, or that a sample statistic does not vary significantly from an assumed population parameter. In other cases we use the null hypothesis to state that one sample distribution does not differ from another (i.e., that they both are from the same population). The alternative hypothesis holds that there is a difference between sample statistics or between a sample statistic and population parameter.
Task 2.3Describe whether and why you used a one-tailed tests or a two-tailed test. (5 P)
A two-tailed test is a significance test in which the alternative hypothesis specifies no direction of difference from the population parameter value such as m. Equal rejection regions are in both tails of the distribution. In a one-tailed test we specify a "less than" or "greater-than" direction to the alternative hypothesis, placing all of a rejection region in one tail, or differing amounts of rejection region in each tail
Task 3TestingHypotheses(20 points in total)
A producer of tires states that the durability of his tires is normally distributed with a mean of 60,000 km and a standard deviation of 6,000 km. To check this statement a sample of 400 tires istaken and a mean durability of 58,400 km is found.
Task 3.1Check with a significance level of 95%, whether the durability stated by the producer is too high.[Don’t forget the interpretation of the result] [7]
-- see XL --
Task 3.2For the premium type tires the average durability is advertised to be 66,000 km. A sample of 625 tires results in an average durability of 66,600 km (s = 6,000). Test with an error probability of 1%, whether the durability of the tires can be 66,000 (and is neither larger nor smaller). [7]
-- see XL --
Task 3.3What’s the confidence interval in the latter test?[3]
-- see XL --
Task 3.4Sketch the test decision of 3.2(in a simple graph). [3]
-- as we did in class --
Task 4Two-Sample Test@ HSB(20 points in total)
In the first exam of this Research Methods class there were two groups of students: 3 MA students from Bremen (B) und 15 international students (I). The average percentage achieved by B was 70.0 with a standard deviation of 25.6 and for I was 75.1 with a standard deviation of 24.8.
Task 4.1You want to know whether both groups of students performed equally. Test this hypothesiswith a confidence level of 95 %. [Don’t forget the interpretation of the result] [8]
Task 4.2Describe the test you just performed in your own words. How does a hypothesis test work? [3]
Task 4.3A lecturer of a private university(financed by tuition fees) is wondering whether he treats the different groups of students equally. Describe the (possible) management dilemma und question and derive a research question and the hypothesis (in words) for the test above (4.1) (9 P)
P. Schmidt -Research Methods (resit 2006)page 1