Listed below are the budgets in millions of dollars and gros

Listed below are the budgets (in millions of dollars) and gross receipts (in millions of dollars) for randomly selected movies. Does there appear to be a linear correlation between the money spent making the movie and the amount that it recovered in theaters? State the null and alternative hypotheses, the pvalue, and conclusion and use a level of significance of .05. You do not have to find a linear regression equation.

Budget       62   90   50   35   200   100   90

Gross         65   64   48   57   601   146   47

Solution

Ho: rho = 0
ha: rho =/= 0 [ANSWER, HYPOTHESES]

Using technology, we get the correlation,              
              
r =    0.925848877          
              
As t = r sqrt [(n - 2) / (1 - r^2)], then as n = 7,              
              
t =    5.478417652          
              
As alpha =    0.05          

df = n - 2 =   5          
              
Then              
              
P = 0.002762362 [ANSWER, P VALUE]
              
As P < 0.05, we reject Ho.

Thus, there is significant evidence that there is a linear correlation between the money spent making the movie and the amount that it recovered in theaters. [CONCLUSION]