Question

# The table below shows a set of bivariate data: X and Y. Calculate the covariance and...

The table below shows a set of bivariate data: X and Y.

1. Calculate the covariance and correlation coefficients by completing the below table, assuming sample data. Show all workings. (Note: You can calculate the mean and standard deviation of X & Y with Excel or your calculator; no working for their calculation is required.)
 X Y (X - X bar) (Y - Y bar) (X - X bar)(Y - Y bar) 5 5 -0.2 -0.6 0.12 2 3 -3.2 -2.6 8.32 5 4 -0.2 -1.6 0.32 8 7 2.8 1.4 3.92 6 9 0.8 3.4 2.72
1. Comment on the direction and strength of the association between X and Y.

Question 2     Simulation Survey

At the end of semester 2 2018, a survey was conducted on BSB123 students’ attitudes toward the tutorial simulation activities. They were asked to state the extent to which they found the simulation activities helpful for their learning in BSB123 on a 7 point scale (1 = strongly disagree; 4 = neutral; 7 = strongly agree). Gender and Lecture Attendance in BSB123 were also recorded. A random sample of 60 students was selected and the sample data are contained in the file: Simulation Survey.xlsx, available on Bb. For ease of data analysis, a new variable: Rating_cat was created to re-group the simulation ratings into three categories: Disagree (1, 2 & 3), Neutral (4), Agree (5, 6 & 7).

1. Using the Pivot Table in Excel cross tabulate Lecture Attendance and Rating_cat. Copy and paste the pivot table onto your answer sheet and use the table to answer the following questions.
 Count of Rating_cat Column Labels Row Labels 10 or more 3 or less 4 to 6 7 to 9 Grand Total Agree 21 4 6 31 Disagree 8 4 1 1 14 Neutral 10 1 1 3 15 Grand Total 39 5 6 10 60

(i) What is the probability that a randomly selected respondent agrees the simulation activities were helpful for their learning?

(ii)   What is the probability that a student who attended 10 or more lectures agrees the simulation activities were helpful for their learning?

(iii) What is the probability that a student who attended 3 or fewer lectures disagrees the simulation activities were helpful for their learning?

(iv) Would you say respondents’ Lecture attendance and Attitude towards simulations activities are dependent or independent? Explain briefly.

A.

 X Y (X - X bar) (Y - Y bar) (X - X bar)(Y - Y bar) (X - X bar)^2 (Y - Y bar)^2 5 5 -0.2 -0.6 0.12 0.04 0.36 2 3 -3.2 -2.6 8.32 10.24 6.76 5 4 -0.2 -1.6 0.32 0.04 2.56 8 7 2.8 1.4 3.92 7.84 1.96 6 9 0.8 3.4 2.72 0.64 11.56