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Sliva [168]
3 years ago
10

Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. Fo

r a sample of 14 stations last Tuesday, the correlation was 0.65. Can the company conclude that the correlation is positive
Mathematics
1 answer:
Semenov [28]3 years ago
6 0

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

     

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