Question

Confirmed Cases CA: 18517, 3315, 2826, 2018, 1845, 1666, 1401, 1340, 1019

Confirmed Cases WA: 5637, 2243, 1212, 923, 383, 330, 293, 283, 282

The data you are being provided with relates to information collected about the current COVID-19 pandemic. You are being asked to analyze this “case” data

Identify Elements of Design

Various procedures used to create an experiment or correlational study (e.g. one-tailed test, random sample, etc...)

Fully demonstrated knowledge of concepts as required.

Answer 1

correlation between CA (x variabele)and WA (y variable)

         x= CA y =WA xy                  x^2         y^2

    18517.0   5637.0 104380329.0 342879289.0 31775769.0

    3315.0   2243.0    7435545.0   10989225.0 5031049.0

     2826.0   1212.0    3425112.0    7986276.0   1468944.0

     2018.0    923.0    1862614.0    4072324.0    851929.0

     1845.0    383.0     706635.0    3404025.0    146689.0

     1666.0    330.0     549780.0    2775556.0    108900.0

     1401.0    293.0     410493.0    1962801.0     85849.0

     1340.0    283.0     379220.0    1795600.0     80089.0

     1019.0    282.0     287358.0    1038361.0     79524.0

sum 33947.0 11586.0 119437086.0 376903457.0 39628742.0

   

                

       (1) Calculation:-   

           

                The pearson correlation coefficient r is computed using the following expression:

           

                     r = n(Σxy)-(Σx)(Σy)/sqrt[nΣx^2-(Σx)^2][nΣy^2-(Σy)^2]

      

                Also we can write it as,   

           

                     r = sigma_xy/sqrt(sigma_x*sigma_y)

       

In this case, based on the data provided, we compute that

sigma_xy = ∑ (xi)(yi) -( Σ xi * Σ yi)/n

= 119437086.0-33947.0*11586.0/9

sigma_xy = 75735991.362

sigma_x = Σ(xi^2) -( Σ(xi)^2)/n

= 376903457.0-33947.0^2/9

sigma_x =248859137.345

sigma_y = Σ(yi^2) -( Σ(yi)^2)/n

= 39628742.0-11586.0^2/9

                    sigma_y =24713705.724

                Therefore, based on this information, the sample correlation coefficient is computed as follows

r = sigma_xy/sqrt(sigma_x*sigma_y)

r = 75735991.362/sqrt(248859137.345*24713705.724)

r = 0.9657

                The following needs to be tested:

                   

      (2) State the Hypotheses:-

                

                    H0: ρ = 0

               

                    Ha: ρ ≠ 0

               

            where ρ corresponds to the population correlation

           

            Null Hypothesis H0: The population correlation coefficient IS NOT significantly different from zero.

                            There IS NOT a significant linear relationship (correlation) between X and Y in the population.

            Alternate Hypothesis Ha:The population correlation coefficient is significantly different from zero.

                            There is a significant linear relationship (correlation) between X and Y in the population.

     (3) Test statistic:-

              

                The sample size is n =9, so then the number of degrees of freedom is df = n-2 = 9 - 2 = 7

               

                The significance level of alpha = 0.05, for a two-tailed test is:

               

                        t_cal=r-ρ*((n-2)/(1-r^2))

               

                But ρ= 0 must be rejected.

               

                Therefore,

               

                        t_cal=r*sqrt((n-2)/(1-r^2))

               

                             = 0.9657*sqrt((9-2)/(1-0.9326))

                   

                        t_cal = 9.8415

       

      (4) Decision criteria:

       

          Using the P_value approach:-

       

            The P_value is 0.0,and since p_value = 0.0 < alpha = 0.05

            It is then concluded that the null hypothesis is rejected

      

    (5) Conclusion:-

           

            It is conclude that the null hypothesis H0 is rejected.

     Therefore,there is enough evidence to conclude that there is a significant linear relationship between

    CA and WA , correaltion coefficient is significantly different from zero"