Call: 1m (formula Brth15to17 PovPct, data poverty) Residuals: Min 1Q Median -11.093 -7.252 1.759 Coefficients: 3Q 6.002 (Intercept) 13.2365 PovPct 0.8216 Max 10.668 Estimate Std. Error t value Pr (> |t|) 12.3744 1.070 0.316 0.8433 0.974 0.358 Residual standard error: 8.422 on 8 degrees of freedom Multiple R-squared: 0.1061, Adjusted R-squared: 0.005676 F-statistic: 0.9492 on 1 and 8 DF, p-value: 0.3585 a) From these data, what is the raw effect size (including units) describing how teen pregnancy rate changes with poverty level across these states? b) What is the 95% confidence interval for this estimate? c) Assuming all assumptions were met and considering only the above information, what should the NGO conclude from their analysis? Explain your answer. d) Is power a potential concern? Explain why or why not.

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2. Data from across counties with a US state of Georgia indicated that teen pregnancy rates tended to increase
with increasing poverty level. In particular, the number of births per 1000 females aged 15-17 years old
increased by 3 for every unit increase in the percentage of a county's residents living in households with
incomes below the federally defined poverty level. A federal non-profit group studying teen pregnancies argued
that such a rate (or higher) would be of concern if it existed more broadly across states. The NGO therefore
collated available data for 10 states for the same two variables (with births and poverty rates being measured at
the state instead of county level). Results of their analysis were as follows (points are individual states):
Brth 15to17
25 30
20
10
=
12
Coefficients:
PovPct
14
PovPct
16
Call:
1m (formula Brth15to17 PovPct, data = poverty)
18
Residuals:
Min
10 Median
3Q
-11.093 -7.252 1.759 6.002
20
Max
10.668
Estimate Std. Error t value Pr (>|t|)
(Intercept) 13.2365 12.3744 1.070
0.8216 0.8433 0.974
0.316
0.358
Residual standard error: 8.422 on 8 degrees of freedom
Multiple R-squared: 0.1061, Adjusted R-squared: 0.005676
F-statistic: 0.9492 on 1 and 8 DF, p-value: 0.3585
a) From these data, what is the raw effect size (including units) describing how teen pregnancy rate changes
with poverty level across these states?
b) What is the 95% confidence interval for this estimate?
c) Assuming all assumptions were met and considering only the above information, what should the NGO
conclude from their analysis? Explain your answer.
d) Is power a potential concern? Explain why or why not.
Transcribed Image Text:2. Data from across counties with a US state of Georgia indicated that teen pregnancy rates tended to increase with increasing poverty level. In particular, the number of births per 1000 females aged 15-17 years old increased by 3 for every unit increase in the percentage of a county's residents living in households with incomes below the federally defined poverty level. A federal non-profit group studying teen pregnancies argued that such a rate (or higher) would be of concern if it existed more broadly across states. The NGO therefore collated available data for 10 states for the same two variables (with births and poverty rates being measured at the state instead of county level). Results of their analysis were as follows (points are individual states): Brth 15to17 25 30 20 10 = 12 Coefficients: PovPct 14 PovPct 16 Call: 1m (formula Brth15to17 PovPct, data = poverty) 18 Residuals: Min 10 Median 3Q -11.093 -7.252 1.759 6.002 20 Max 10.668 Estimate Std. Error t value Pr (>|t|) (Intercept) 13.2365 12.3744 1.070 0.8216 0.8433 0.974 0.316 0.358 Residual standard error: 8.422 on 8 degrees of freedom Multiple R-squared: 0.1061, Adjusted R-squared: 0.005676 F-statistic: 0.9492 on 1 and 8 DF, p-value: 0.3585 a) From these data, what is the raw effect size (including units) describing how teen pregnancy rate changes with poverty level across these states? b) What is the 95% confidence interval for this estimate? c) Assuming all assumptions were met and considering only the above information, what should the NGO conclude from their analysis? Explain your answer. d) Is power a potential concern? Explain why or why not.
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