The World Bank collects information on the life expectancy of a person (dependent) in each country ("Life expectancy at," 2013) and the fertility rate per woman (independent) in the country ("Fertility rate," 2013). The data for 24 randomly selected countries for the year 2011 are in the table below.
In the chapter 4 homework quiz, you found that this relationship was linear, negative and of strong strength level with a correlation coefficient of -0.9313. The line of best-fit is predicted life expectancy = -4.706(fertility rate) + 84.873. Now, test the relationship at a significance level of 0.05 to answer the question: Is there enough evidence to show that there is a linear relationship between fertility rate and life expectancy?
Use the framework below to guide your work.
Hypotheses: :
Ho: Beta or pho = 0 (no linear relationship)
Ha: Beta or pho not equal to 0 (linear relationship)
Blank #1: Test statistic = _________ (round to two decimal places)
Blank #2: p-value = __________ (round to four decimal places)
Blank #3: Test decision: We decide to ___________ Ho (reject or do not reject)
Blank #4: Conclusion back into the words of problem: The evidence __________(favors or does not favor) that there is a linear relationship between fertility rate and life expectancy.
Blank #5: Previously, you had made a prediction of 72.17 years life expectancy for a country with a fertility rate of 2.7 per woman. Is this a prediction that should be made based on the results of the significance test? (yes or no)
Fertility Rate |
Life Expectancy |
1.7 |
77.2 |
5.8 |
55.4 |
2.2 |
69.9 |
2.1 |
76.4 |
1.8 |
75.0 |
2.0 |
78.2 |
2.6 |
73.0 |
2.8 |
70.8 |
1.4 |
82.6 |
2.6 |
68.9 |
1.5 |
81.0 |
6.9 |
54.2 |
2.4 |
67.1 |
1.5 |
73.3 |
2.5 |
74.2 |
1.4 |
80.7 |
2.9 |
72.1 |
2.1 |
78.3 |
4.7 |
62.9 |
6.8 |
54.4 |
5.2 |
55.9 |
4.2 |
66.0 |
1.5 |
76.0 |
3.9 |
72.3 |
2
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