THA 2 - BSB123 - THA 2 - GPA 7 PDF

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THA 2 - GPA 7...

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THA 2 – BSB123 Jordan Scanlan | N10077634 Q1) Calculate by hand the covariance and correlation coefficient of the following set of bi-variate data, assuming they are sample data. Show all workings. (You can calculate the mean and standard deviation of X & Y with the STAT mode in your calculator and no working is required of their calculation.) -

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Mean of X = 25 Mean of Y = 24 X Y (X – X BAR) 4 8 (4 – 25) = - 21 2 7 (2 – 25) = - 23 5 6 (5 – 25) = - 20 8 2 (8 – 25) = - 17 6 1 (6 – 25) = - 19

(Y – Y BAR) (8 – 24) = - 16 (7 – 24) = - 17 (6 – 24) = - 18 (2 – 24) = - 22 (1 – 24) = - 23

(X – X BAR)(Y – Y BAR) 336 391 360 374 437

Σ=2335 x−x ¯¿ ¿ y− y ¯¿ ¿ Σ¿ Cov ( X , Y ) =¿

Q2) A survey was carried out to gather information about people’s opinions about capital punishment on a 5-point scale (1 = strongly disagree; 2= disagree; 3 = neither agree nor disagree; 4 = agree; 5 = strongly agree). Demographic characteristics about the respondents were also collected in the survey. A) Use the Pivot Table in Excel to cross tabulate Education and Opinion. Copy and paste the contingency table onto your answer sheet and use the table to answer the following questions. (Show your workings as appropriate.) Row Labels P 1 2 3 S 1 2 3 4 5 U 1 2 3

Count of Education

Count of Opinion 5 1 2 2 17 1 1 3 6 6 18 5 4 2

5 1 2 2 17 1 1 3 6 6 18 5 4 2

4 5 Grand Total

4 3 40

4 3 40

1. (i) What is the probability that a randomly selected respondent strongly disagree with capital punishment? Opinion Sample = {1, 2, 3, 4, 5) P(Strongly disagree) = 1/5 = 20% 2. (ii) What is the probability that a respondent with only high school qualification strongly disagrees with capital punishment? Education Probability (P, S, U) P(S) = 1/3 = 33.333% Opinion Sample (1, 2, 3, 4, 5) P(Strongly disagree) = 1/5 = 20% According to pivot table. P(High school (S) that strongly disagrees (1)) = 1 out of 17 high schoolers. = 5.882% 3. (iii) Would you say respondents’ Opinion and Education are dependent or independent? Dependant. B) Use the Pivot Table to calculate the average opinion of the male and female respondents and comment in one sentence the relationship between Gender and Opinion? Row Labels F 1 2 3 4 5 M 1 2 3 4 5 Grand Total

Sum of Opinion

Average of Opinion2 57 4 6 18 4 25 70 3 8 3 36 20 127

Average opinion of Females is 3 Average opinion of Males is 3.33333

3 1 2 3 4 5 3.333333333 1 2 3 4 5 3.175

Which would suggest that there is a strong correlation between the two genders as they both have similar general senses. C) Create a scatter plot to display the relationship between Age and Opinion and use Excel to compute their correlation coefficient. Comment on the strength of their relationship.

Age and Opinion 6 5

OPINION

4 3 2 1 0 15

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AGE

Examining the scatter plot, it looks to have a positive linear slope however the results suggest that its strength is quite weak, so although it has a positive correlation, it is a weak correlation....