Questions: 9 of 9 Do abandoned children placed in foster homes do better than similar children placed in an institution? The Bucharest Early Intervention Project found statistically significant evidence that they do. The subjects were 136 young children abandoned at birth and living in orphanages in Bucharest, Romania. Half of the children, chosen at random, were placed in foster homes. The other half remained in the orphanages. (Foster care was not easily available in Romania at the time and so was paid for by the study.) What conclusion can be drawn from this study? We can infer that the difference between foster care and institutional care caused the difference in response. Also, the results can be applied to children beyond the ones in the study. We cannot infer that the difference between foster care and institutional care caused the difference in response. However, the results can be applied to children beyond the ones in the study. We cannot include anything because of the bias created by the study paying for the foster care. We can infer that the difference between foster care and institutional care caused the difference in response. However, the results should only be applied to children like the ones in the study. We cannot infer that the difference between foster care and institutional care caused the difference in response. Furthermore, the results should only be applied to children like the ones in the study.

9 of 9 Do abandoned children placed in foster homes do better than similar children placed in an institution? The Bucharest Early Intervention Project found statistically significant evidence that they do. The subjects were 136 young children abandoned at birth and living in orphanages in Bucharest, Romania. Half of the children, chosen at random, were placed in foster homes. The other half remained in the orphanages. (Foster care was not easily available in Romania at the time and so was paid for by the study.) What conclusion can be drawn from this study? We can infer that the difference between foster care and institutional care caused the difference in response. Also, the results can be applied to children beyond the ones in the study. We cannot infer that the difference between foster care and institutional care caused the difference in response. However, the results can be applied to children beyond the ones in the study. We cannot include anything because of the bias created by the study paying for the foster care. We can infer that the difference between foster care and institutional care caused the difference in response. However, the results should only be applied to children like the ones in the study. We cannot infer that the difference between foster care and institutional care caused the difference in response. Furthermore, the results should only be applied to children like the ones in the study.
Transcript text: 9 of 9 Do abandoned children placed in foster homes do better than similar children placed in an institution? The Bucharest Early Intervention Project found statistically significant evidence that they do. The subjects were 136 young children abandoned at birth and living in orphanages in Bucharest, Romania. Half of the children, chosen at random, were placed in foster homes. The other half remained in the orphanages. (Foster care was not easily available in Romania at the time and so was paid for by the study.) What conclusion can be drawn from this study? We can infer that the difference between foster care and institutional care caused the difference in response. Also, the results can be applied to children beyond the ones in the study. We cannot infer that the difference between foster care and institutional care caused the difference in response. However, the results can be applied to children beyond the ones in the study. We cannot include anything because of the bias created by the study paying for the foster care. We can infer that the difference between foster care and institutional care caused the difference in response. However, the results should only be applied to children like the ones in the study. We cannot infer that the difference between foster care and institutional care caused the difference in response. Furthermore, the results should only be applied to children like the ones in the study.
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Solution

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Solution Steps

Step 1: Standard Error Calculation

The Standard Error \( (SE) \) is calculated using the formula:

\[ SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} = \sqrt{\frac{37.0667}{10} + \frac{7.0667}{10}} = 2.1008 \]

Step 2: Test Statistic Calculation

The test statistic \( (t) \) is computed as follows:

\[ t = \frac{\bar{x}_1 - \bar{x}_2}{SE} = \frac{86.8 - 71.8}{2.1008} = 7.1402 \]

Step 3: Degrees of Freedom Calculation

The degrees of freedom \( (df) \) are calculated using the formula:

\[ df = \frac{\left(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}\right)^2}{\frac{\left(\frac{s_1^2}{n_1}\right)^2}{n_1 - 1} + \frac{\left(\frac{s_2^2}{n_2}\right)^2}{n_2 - 1}} = \frac{19.4775}{1.5821} = 12.3113 \]

Step 4: P-value Calculation

The p-value is calculated as:

\[ P = 2(1 - T(|t|)) = 2(1 - T(7.1402)) = 0.0 \]

Step 5: Conclusion

Since the p-value \( (0.0) \) is less than the significance level \( (0.05) \), we can conclude that there is a statistically significant difference between the two groups. Therefore, we can infer that the difference between foster care and institutional care caused the difference in response. However, the results should only be applied to children like the ones in the study.

Final Answer

\(\boxed{\text{We can infer that the difference between foster care and institutional care caused the difference in response. However, the results should only be applied to children like the ones in the study.}}\)

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