BRCA1 is a gene whose mutation is linked to breast cancer. Researchers used DNA analysis to search for this gene in 150 women with family histories of breast cancer. 22 of these women had the BRCA1 mutation.

Using the plus 4 method:

1. What is the sample proportion of women with family history of breast cancer that has the BRCA1 mutation?
2. Standard error for the proportion of all women with a family history of breast cancer that have the BRCA1 mutation is?
3. Margin of error of a 95% confidence interval for proportion of all women with a family history of breast cancer that have the BRCA1 mutation is?
4. A one sided test of significance at 5% was performed to decide if more than 10% of such women carry this BRCA1 mutation. The result was a p value of 0.0283, what is the conclusion?