Question

1. A car dealer wants to examine the relationship between the number of TV ads run per week and the number of cars sold per week. Suppose a sample of 6 weeks shows that the correlation coefficient is 0.828. Is there a statistically significant relationship between the number of ads and the number of cars sold? Test using α=0.05.
   1. Set up the null and alternate hypotheses.
2. 2. Calculate an appropriate test statistic.

                  c.What is the p-value? Explain your conclusion in the context of the question.

Answer 1

The following needs to be tested:

H_0: = 0

H_A: 0

where corresponds to the population correlation.

The sample size is n = 6 , so then the number of degrees of freedom is df = n - 2 = 6 - 2 = 4.

test dtatistc, t =

t =

t =

t = 2.89

t_critical for two tailed test = 2.776

Since, |t| = 2.89 > t_c = 2.776 , null hypothesis is rejected

Using , p value = 0.954

Since, p > alpha ( 0.05 ), we reject null hypothesis.

Hence the correlation is not equal to 0