Question

2. A researcher is interested in the relationship between hours spent studying per day and the number of class tests passed. A random sample of 4 participants are selected from the Statistics for Social Sciences class. Manually compute and interpret the Pearson correlation for the following data using a two-tailed test and a = 0,05. (15 Marks) Hours spent studying Class tests passed 2 3 3 6 5 1

may I have it written down with a pen please step by step

Answer 1

Solution

Now, with the provided sample data, we need to construct the following table to compute the correlation coefficient: Obs. X Y x X; Y; 1 2 3 4 9 6 3 1 9 1 3 N 3 6 5 36 25 30 4 4 4 16 16 16 Sum = 15 13 65 51 55 Based on the table above, we compute the following sum of squares that will be used in the calculation of the correlation coefficient: 2 n n 1 SSxx = ΣΧ; n i=1 = 65 1 x 225 4. = 8.75 n n 1 SSYY Y? ΣΥ n i=1

1 51 x 169 4 8.75 n 1 SSXY X; Y; (2x) (8) n i=1 55 1 4 X 195 = 6.25 Now, the correlation coefficient is computed using the following expression: SSXY r SSXX SSyy = 6.25 18.75 x 8.75 = 0.7143

The following needs to be tested: H:p=0 HA :p=0 where p corresponds to the population correlation. The sample size is n = 4, so then the number of degrees of freedom is df = n – 2 = 4 – 2 = 2 The corresponding t-statistic to test for the significance of the correlation is: n - 2 1 p2 = 0.7143 V 4-2 1-0.71432 = 1.443 The p-value is computed as follows: p= Pr(t2 > 1.443) = 0.2857 Since we have that p=0.2857 > 0.05, it is concluded that the null hypothesis Ho is not rejected.

Therefore, based on the sample correlation provided, it is concluded that there is not enough evidence to claim that the population correlation ρ is different than 0, at the 0.05 significance level.