Question

Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65. Can the company conclude that the correlation is positive

Answer 1

Complete Question

Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65.At the 0.01 significance level Can the company conclude that the correlation is positive

Answer:

Yes the company conclude that the correlation is positive

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  14

    The correlation is  r =  0.65

     

The  null hypothesis is  $H_o : r < 0$

The  alternative hypothesis is  $H_1 : r > 0$

Generally the standard deviation is mathematically evaluated as

       $Sr = \sqrt{1- r}$

       $Sr = \sqrt{1- 0.65}$

       $Sr = 0.616$

The  degree of freedom for the one-tail test is

       $df = n- 2$

        $df = 14- 2$

        $df = 12$

The standard error is evaluated as

        $SE = \frac{0.616}{ \sqrt{12} }$

        $SE =0.1779$

The test statistics  is evaluated as

      $t = \frac{r }{SE}$

       $t = \frac{0.65 }{0.1779}$

        $t = 3.654$

The p-value of of  t is obtained from the z table, the value is  

        $p-value = P(t < 3.654) = 0.00012909$

Given that $p-value < \alpha$  then we reject the null hypothesis

           Hence the company can conclude that the correlation is positive