Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information:
Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information:
| x | 1 | 2 | 3 | 4 | 5 |
| y | 12.2 | 20.9 | 14.4 | 19.6 | 20.0 |
Σx = 15; Σy = 87.1 ; Σx2 = 55; Σy2 =1577.17; Σxy = 275.6
(a) Draw a
(b) Find the equation of the least-squares line. (Round your answers to two decimal places.)
| ŷ = | + x |
(c) Find r. Find the coefficient of determination r2. (Round your answers to three decimal places.)
| r = | |
| r2 = |
Explain what these measures mean in the context of the problem.
The
The coefficient of determination r measures the strength of the linear relationship between a bighorn sheep's age and the mortality rate. The correlation coefficient r2 measures the explained variation in mortality rate by the corresponding variation in age of a bighorn sheep.
Both the correlation coefficient r and coefficient of determination r2 measure the strength of the linear relationship between a bighorn sheep's age and the mortality rate.
The correlation coefficient r2 measures the strength of the linear relationship between a bighorn sheep's age and the mortality rate. The coefficient of determination r measures the explained variation in mortality rate by the corresponding variation in age of a bighorn sheep.
(d) Test the claim that the population correlation coefficient is positive at the 1% level of significance. (Round your test statistic 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 that ρ> 0.
Reject the null hypothesis, there is insufficient evidence thatρ > 0.
Fail to reject the null hypothesis, there is sufficient evidence that ρ > 0.
Fail to reject the null hypothesis, there is insufficient evidence that ρ > 0.
(e) Given the result from part (c), is it practical to find estimates of y for a given x value based on the least-squares line model? Explain.
Given the lack of significance of r, prediction from the least-squares model might be misleading.
Given the significance of r, prediction from the least-squares model is practical.
Given the significance of r, prediction from the least-squares model might be misleading.
Given the lack of significance of r, prediction from the least-squares model is practical.
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