Question: Helping welfare mothers. A study compares two groups of mothers with young children who were on welfare two years ago. One group attended a voluntary training program that was offered free of charge at a local vocational school and was advertised in the local news media. The other group did not choose to attend the training program. The study finds a significant difference (p < 0.01) between the proportions of the mothers in the two groups who are still on welfare. The difference is not only significant but quite large. The report says that with 95% confidence the percent of the nonattending group still on welfare is 21% \(\pm \) 4% higher than that of the group who attended

1. Explain in simple language what "a significant difference (p < 0.01)" means.
2. Explain clearly and briefly what "95% confidence" means.
3. Is this study good evidence that requiring job training of all welfare mothers would greatly reduce the percent who remain on welfare for several years?

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