Business statistics

Analysis Report

Date Due: Week 14 (20th of October 2023; 5pm)

Total Marks: 30 marks Worth: 30% of final assessment

You need to prepare an analysis report (using Microsoft Word), which requires an amount of computer work and written comment. Each task describes what you are required to do, so please follow these instructions carefully!

In this report, you will analyse a student survey. It has four selected variables, namely gender (with categories of female and male), race (with categories of african american, asian, hispanic, and white), math (Standardized math score) and socst (Standardized social studies score).

Task 1: Use the Chi-square test at the 10% level of significance to determine whether gender and race are independent. The following table can be used: (15 Marks)

a. Create the contingency table to show student’s frequencies of the gender and race variables. Calculate the row totals, column totals and total frequency. (5 Marks)

gender	race
	African American	Asian	Hispanic	White	Total
female
male
Total

b. State the null and alternative hypotheses. (2 Mark)

c. Calculate expected values. (3 Marks)

gender	race
	African American	Asian	Hispanic	White	Total
female
male
Total

d. Calculate the test statistics. 3 Marks)

e. State the rule of decision. (1 Mark)

f. State the conclusion. (1 Mark)

Task 2: Perform the regression analysis of the math variable on the socst variable. The following table can be used for part (e): (15 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 socst and math variables respectively. (3 Marks)

b. Create a scatter plot using math and socst variables as the x-axis and the y-axis respectively. (2 Marks)

c. Determine and interpret the Coefficient of Determination, i.e., R square. (2 Marks)

d. Determine the regression equation. Interpret the slope. (3 Marks)

e. Perform the hypothesis test to determine if the slope is significantly differently from zero at 5% significance level. (5 Marks)