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 percentage of the nonattending group still on welfare is 21% ± 4% higher than that of the group who attended the program. You are on the staff of a member of Congress who is interested in the plight of welfare mothers and who asks you about the report.

(a) Explain in simple language what “a significant difference (P < 0.01)” means.

(b) Explain clearly and briefly what “95% confidence” means.

(c) This study is not good evidence that requiring job training of all welfare mothers would greatly reduce the percentage who remain on welfare. Explain this to the member of Congress.