Question

4) The table below shows the life expectancy for an individual born in the United States in certain years. Year of Birth Life Expectancy (a) Use the Rossman Chance applet to find the sample correlation coefficient 1930 59.7 1940 62.9 (b) What does the correlation coefficient imply about the relationship between year of birth and life expectancy? 1950 70.2 1965 69.7 (e) We want to know if this data provides strong evidence of correlation between the year of birth and life expectancy. Write the null and alternative 1973 71.4 hypotheses in symbols, and also in words. 1982 74.5 (d) Conduct a simulation in the Rossman Chance applet to find a p-value. 1987 75 Complete the following sentence in context of the problem: "If we assume 1992 75.7 then the probability of 2010 78.7 (e) Write a conclusion in context. Le write a conclusion like "we have strong evidence that." or "it is plausible that... ( Use the applet to find the t-score and p-value with a theory-based approach. Do we make the same conclusion that was made in part (e)? (g) Would you feel confident using the regression equation to get a fairly accurate estimate of the life expectancy of a person based on their year of birth? Explain is Solution for (a): Solution for (b): Solution for (c): Solution for (d): Solution for (e): Solution for (f): Solution for (b):

Answer 1

Sol:

In Excel type all data ,

To run regression data-data analysis- regression- choose all x and y values- ok

Here life expectancy depends on the year of birth so

We take y as expectancy , and x as the year of birth

So from out put we get

y^ = -377.243 + 0.22748 * x

So

a)

-377.243

b)

b = 0.22748

c)

r= multiple R = 0.961261

d )

p value = 0.0000363

Here alpha =0.05

So p value < alpha

e) x = 1950

So estimated expectancy y^ = -377.243 + 0.22748 * 1950 =66.34235

f) x= 1982

then estimated life expectancy for an individual born in 1982 =y^ = -377.243 + 0.22748 * 1982= 73.6217

1 SUMMARY OUTPUT 2 3 Regression Statistics 4 Multiple R 0.961261 5 R Square 0.924023 6 Adjusted R S 0.913169 7 Standard Error 1.820233 8 Observations 9 9 10 ANOVA df Significance 3.62726E-05 12 Regression 3 Residual 14 Total SS MS F 1 282.0673 282.0673 85.133 7 23.19273 3.313247 8 305.26 16 17 Intercept 18 X Variable 1 Coefficientandard Err t Stat P-value -377.243 48.57009 -7.76698 0.0001 0.22748 0.024654 9.226764 46-05 Lower 95% Upper 95%ower 95.09pper 95.0% -492.0931111 -262.393 1492.093 -262.393 0.169181482 0.285778 0.169181 0.285778 20

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