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- From: Mathematics, Statistics and Probability
- Posted on: Sat 23 Jan, 2016
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This exercise requires you to use an electronic spreadsheet, such as Microsoft's Excel, to compute information about a data set. The data set is shown in Table 1 below. There are three groups in the complete data set:
Group 1—Learning via the Lecture method of instruction
Group 2—Learning via the Cooperative method of instruction
Group 3—Learning via Computer-based instruction
The scores in each group are the final examination scores of students in the three groups. The scores represent overall knowledge learned under each method of instruction. The higher the score, the more knowledge learned. The Independent and Dependent variables are:
Independent variable - the method of instruction at three levels: Lecture, Cooperative, and Computer.
Dependent variable - the final examination score.
GROUP1 (LECTURE)
78
88
96
77
83
85
90
85
95
68
a. Compute the descriptive statistics for Group 1.
b. Calculate the correlation coefficient between Groups 1 and 2.
c. Perform a t-Test between Groups 1 and 2.
For the case of Groups 1 and 2, we want to know whether any significant difference exists between the mean values for these groups. Statistically speaking, we are asking is the observed absolute difference between the mean values of Group 1 and Group 2 due to treatment effect, or is it due to chance? Assuming the sample is a perfectly good random sample, the t-Test is the appropriate statistic.
d. Perform an analysis of variance (ANOVA).
The ANOVA test will tell us if there is a significant difference between the means of respective groups.
Use the F – statistic for AVOVA testing.
Question 2
You are interested in conducting a descriptive study of the riders of Harley Davidson motorcycles. Complete an analysis of this population’s structure and characteristics. Respond to each question on the checklist and prepare your response.
1. Identify the particular population you have chosen:
2. Now answer the following questions with respect to the structure of the population:
a. Is the population a relatively homogeneous group of individuals or other units? Yes ____
b. Could the population be considered to consist generally of equal “layers,” each of which is fairly homogeneous in structure? Yes ________ No ___________
c. Could the population be considered to be composed of separate homogeneous layers differing in size and number of units comprising them? Yes ______ No ______
d. Could the population be envisioned as isolated islands or clusters of individual units, with the clusters being similar to one another in composition? Yes ________ No ___________
3. Through what means would you extract a representative sample from the total population? Describe your procedure.
4. Is your sampling procedure appropriate for the characteristics of the population? Yes _______
5. Have you guaranteed that your sample will be chosen by chance and yet will the representative of your population? Yes ______ No __________
6. If the preceding answer is yes, explain how this will be done.
7. Indicate what means will be employed to obtain the information you need from the sample.
8. What are the weaknesses inherent in this method of obtaining the data?
9. What safeguards have you established to counteract any potential bias in your approach to data collection? Be specific.
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