Bighorn sheep are beautiful wild animals found throughout thewestern United States. Let x be the age of a bighorn sheep(in years), and let y be the mortality rate (percent thatdie) for this age group. For example, x = 1, y =14 means that 14% of the bighorn sheep between 1 and 2 years olddied. A random sample of Arizona bighorn sheep gave the followinginformation:

x	1	2	3	4	5
y	12.8	20.9	14.4	19.6	20.0

Σx = 15; Σy = 87.7; Σx² =55; Σy² = 1592.17; Σxy = 276.2

(a) Draw a scatter diagram.

(b) Find the equation of the least-squares line. (Round youranswers to two decimal places.)

Å· =

+   x

(c) Find r. Find the coefficient of determinationr². (Round your answers to three decimalplaces.)

r =
r2 =

Explain what these measures mean in the context of the problem.

The correlation coefficient r measures the strength ofthe linear relationship between a bighorn sheep's age and themortality rate. The coefficient of determinationr² measures the explained variation inmortality rate by the corresponding variation in age of a bighornsheep.

The coefficient of determination r measures thestrength of the linear relationship between a bighorn sheep's ageand the mortality rate. The correlation coefficientr² measures the explained variation inmortality rate by the corresponding variation in age of a bighornsheep.  

Both the correlation coefficient r and coefficient ofdetermination r² measure the strength of thelinear relationship between a bighorn sheep's age and the mortalityrate.

The correlation coefficient r² measures thestrength of the linear relationship between a bighorn sheep's ageand the mortality rate. The coefficient of determination rmeasures the explained variation in mortality rate by thecorresponding variation in age of a bighorn sheep.

(d) Test the claim that the population correlation coefficient ispositive at the 1% level of significance. (Round your teststatistic to three decimal places.)

t =

Find or estimate the P-value of the test statistic.

P-value > 0.250

0.125 < P-value < 0.250   

0.100 < P-value < 0.125

0.075 < P-value < 0.100

0.050 < P-value < 0.075

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

0.0005 < P-value < 0.005

P-value < 0.0005

Conclusion

Reject the null hypothesis, there is sufficient evidence thatρ > 0.

Reject the null hypothesis, there is insufficient evidence thatρ > 0.   

Fail to reject the null hypothesis, there is sufficient evidencethat ρ > 0.

Fail to reject the null hypothesis, there is insufficientevidence that ρ > 0.

(e) Given the result from part (c), is it practical to findestimates of y for a given x value based on theleast-squares line model? Explain.

Given the lack of significance of r, prediction fromthe least-squares model might be misleading.

Given the significance of r, prediction from theleast-squares model is practical.  

Given the significance of r, prediction from theleast-squares model might be misleading.

Given the lack of significance of r, prediction fromthe least-squares model is practical.