Quantitative Data Analysis

1. A researcher is interested in the prediction of ‘class tests passed’ using ‘hours spent studying per day’ among students of a module at Cornerstone Institute. A random sample of 4 participants was selected from the Research Methods and Statistics class.

Hours spent studying

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Class tests passed

2

3

3

1

6

5

4

4

a. Manually compute the slope (b) and y-intercept for the following data. (12

Marks)

b. Write down the Regression equation for these scores using the slope and yintercept obtained in a) (3 marks)

c. Given a score of 8 hours spent studying, predict the number of class tests passed. (5 marks)

2. A researcher would like to know whether there is a consistent, predictable relationship between verbal skills and math skills for high school students. A sample of 200 students is obtained, and each student is given a standardized English test and a standardized math test. Based on the test results, students are classified as high or low for verbal skills and for Mathematics skills. The results are summarized in the following frequency distribution:

Verbal skills

High

Low

Mathematics

skills

High

59

41

Low

31

69

a. Based on these results, can the researcher conclude that there is a significant relationship between verbal skills and math skills? Test at the .05 level of significance. (Use manual computations and show all calculations) (15 Marks)

b. Calculate strength of the relationship between the two variables of verbal skills and mathematics skills. (5 marks)

3. Mrs Ndlovu is worried about Mulalo’s and the other students’ performance in their performance in Natural Science class. She decides that it is time for an intervention and develops a new portion that increases the students’ motivation to study. She uses the new technique before the second Natural Science test and decides to compare these scores with the scores from the first test to see if it worked as well as he expected.

Student 1

Test 1 score

Test 2 score

1

56

72

2

45

50

3

78

80

4

76

76

5

70

75

6

67

72

7

71

72

8

69

65

9

68

75

10

55

65

a. Compute an appropriate t-statistic in Excel to test if the new technique increase performance in Natural Science (α = .05). Show all your hypothesis testing steps and Excel output. (10 Marks)

b. Calculate the effect size using Estimated Cohen’s d (5 marks)

c. The school Principal advised you to run a test in Excel assuming that the two set of scores were from two different samples. Use significant level of .01: onetailed. Show all your hypothesis testing steps and manual calculations (15 marks)

4. South Africans are known for having a sense of humour about current affairs, but sometimes the public misunderstand the jokes. A local satire news source released an article stating that one of the long-term effects of the coronavirus is mutation into a zombie. Understandably, a lot of people panicked. You, a sensible-minded researcher, decide to assess just how bad these panic levels are. Below is the data you capture from two samples of ten people each, the other on Monday and another on a Friday.

Monday

Friday

3

6

5

7

3

3

1

5

6

8

8

6

2

4

5

5

3

8

4

9

a. Manually perform an appropriate test, at α = .05, to assess if there is a significant difference between the two samples. Show all four steps of hypothesis testing.

(20 marks)

b. Calculate the percentage of variance accounted for by the difference between

Monday and Friday (5 marks)

c. Under what circumstances do researchers make use of Mann Whitney U test? Provide any two relevant examples to clarify your answer. (5 marks)

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