Question

Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 21 stations last Tuesday, the correlation was 0.25. State the decision rule for 0.10 significance level. (Round your answer to 3 decimal places.) Compute the value of the test statistic. (Round your answer to 3 decimal places.) Can we conclude that the correlation in the population is greater than zero? Use the 0.10 significance level.

Answer 1

Here we have n = 21, r = 0.25, = 0.10

The hypothesis are

H0 : 0 v/s H1 : > 0

The decision rule :

df = n-2 = 21-2 = 19, = 0.10

The right tailed critical value is,

( use excel formula "=t.inv( 0.10,19)" )

Critical region is area above t_0.10,19 .

We reject null hypothesis, if calculated value of t lies in the critical region.

The test statistic is,

= 1.125

Here calculated value of t does not lie in the critical region. Hence we fail to reject null hypothesis.

Conclusion :

We conclude that the correlation in the population is not greater than zero.