The number of deaths due to firearms in the United States between 1968 and 1993

Question

The number of deaths due to firearms in the United States between 1968 and 1993 are given in the Excel file.

year   firearm deaths (thousands)
1968   23
1969   24
1970   27
1971   29
1972   30
1973   31
1974   33
1975   32
1976   30
1977   32
1978   31
1979   33
1980   34
1981   34
1982   33
1983   30
1984   31
1985   32
1986   34
1987   33
1988   34
1989   35
1990   37
1991   39
1992   38
1993   41

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 place

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?

Explanation / Answer

a)

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

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b)

Here, n = 26, so

df = n - 2 = 24 [ANSWER]

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c)      

If we assume alpha = 0.05, then at df = 24,

tcrit = 2.064 [ANSWER]

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d)
              
              
As t = r sqrt [(n - 2) / (1 - r^2)], then              
              
t =    8.247094916          
              
As t > 2.064, there is significant trend in firearm deaths over this period. [CONCLUSION]          

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