Explain Terms...

#1
Am I correct?

Q:

A study compares two groups of mothers with young children who were on welfare two years ago. One group attended a voluntary training program offered free of charge at a local vocational school 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% ± 4% higher
than that of the group that 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 briefly and in nontechnical language what “a significant difference (p < 0.01)” means.

A “significant difference (P < 0.01)” means that at P = 0.01, the difference between the two groups has only a 1% probability of occurring by chance alone. Having P = 0.01 also means the difference between the two groups is statistically significant as it can not be explained by chance alone.

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

“95% confidence” means that if you draw repeated, same-sized samples from a population and calculated their confidence intervals, 95% of these intervals should contain the population mean.

c) 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? Why or why not?

This study is good evidence that requiring job training of all welfare mothers would greatly reduce the percent who remain on welfare for several years..... I think this because the p value shows that the difference cannot be explained by chance? Does that make sense?

Just wondering if I've answered this correctly.

Merci :)
 

JohnM

TS Contributor
#2
a) if Ho were actually true, the probability that we obtained our actual result (or larger) is 0.01, therefore there is enough evidence to reject the notion of equivalence between the groups

b) perfect

c) yes, but you need to take into account whether a non-statistician would think that the difference is meaningful (real-world meaningful, not just from a probability perspective) - in other words, is the difference "large enough" to convince someone with decision-making power that the program is "worth it"