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Analysis Report

Task Description

In this report, you will analyse a student survey. It has four selected variables, namely ses (Socio economic status of student’s family, with categories low, middle, and high), schtyp (Type of school, with categories public and private), math (Standardized math score) and science (Standardized science score).


Task 1: Identify data type (4 Marks)
Identify each variable (i.e., ses, schtyp, math and science) in the dataset whether it is categorical nominal, categorical ordinal, quantitative discrete or quantitative continuous.

Task 2: Use the Chi-square test at the 5% level of significance to determine whether schtyp and ses are independent. (10 Marks)

a. Create the contingency table to show student’s frequencies of the schtyp and ses variables. (3 Marks)
b. State the null and alternative hypotheses. (1 Mark)
c. Calculate expected values. (2 Marks)
d. Calculate the test statistics. 2 Marks)
e. State the rule of decision. (1 Mark)
f. State the conclusion. (1 Mark)

Task 3: Perform the regression analysis of the math variable on the science variable. (10 marks)

a. Use the Excel Regression function in the Data Analysis Tools Add-ins to create a simple regression model. The straight-line equation is y = a + bx where y and x are the science and math variables respectively. (3 Marks)
b. Determine and interpret the Coefficient of Determination, i.e., R square. (2 Marks)
c. Determine the regression equation. Interpret the slope. (2 Marks)
d. Perform the hypothesis test to determine if the slope is significantly differently from zero at 5% significance level. (3 Marks)

Conclusion: (6 marks)

From the Chi-square test, you would be able to conclude whether the relationship between schtyp and ses are independent. Also, the regression result would show whether math is a significant predictor for science. Write a short report summarising your main findings.

Solution

Task 1

Variable NameData Type
SesCategorical Ordinal
SchtypCategorical Nominal
MathQuantitative Discrete
ScienceQuantitative Discrete

Task 2

(a)

Contingency Table
 
 Socio-Economic Status of Students’ FamilyTotal
LowMiddleHigh
Type of SchoolPublic447045159
Private2181131
     
Total468856190

(b)

Null hypothesis: H0 :School type is independent of Socio-Economic status of students’ family

Alternative hypothesis: H1: School type is dependent of Socio-Economic status of students’ family 

c) Expected Values

(d) The formula for calculating a Chi-square statistic is:

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