The number of deaths due to firearms in the United States be

The number of deaths due to firearms in the United States between 1968 and 1993 are given in the Excel file.
Answer the following using the research hypothesis, \"there is a correlation between year and number of firearm deaths in the US.\"

A. What is the value of the correlation coefficient between year and number of firearm deaths?  (Answer to 3 decimal places)

B. How many degrees of freedom does your data have?

C. What is the critical value of your test statistic?

D. Is there evidence of a significant trend in firearm deaths over this period?  (yes/no)

Here is the Data. I cant figure this out, please help Thanks!

( 322 29 30 3 3 3 30 333 34 34 3 30 31 3 34 3 34 35 33 t222 23 3333333 B 345678911 12 13 4 5 6 7 8 9 2 2 2 2 2 2 2 12

Solution

a)

Using technology, we get the correlation,                  
                  
r =    0.859750984   [ANSWER]          
                  

b)

df = n - 2 = 26 - 2 =     24 [ANSWER]

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c)
              
If we set this to have a significance of 0.05, as

df =    24              
                  
Then                  
                  
tcrit =    2.063898562   [ANSWER]

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d)          
                  
As t = r sqrt [(n - 2) / (1 - r^2)], then                  
                  
t =    8.247094916              
                  
                  
As t > tcrit, then there is evidence of a significant trend in firearm deaths over this period. [ANSWER, YES]