Question

A study reported by the Women’s Health Initiative gives the following values for the occurrence of breast cancer in women. All women in the study were between 50 and 79 years of age. 19,541 women were randomly assigned to a low-fat diet, and 29,294 were assigned to a control group which ate a normal diet. After 8 years, 655 of the low-fat diet group had developed breast cancer, and 1072 of the women in the control group had developed breast cancer.

1. Create both in symbolic form and in a sentence the null hypothesis that should be used to determine if there is a difference between the two diet groups in the proportions of women who developed breast cancer.
2. Create both in symbolic form and in a sentence the alternative hypothesis that should be used to determine if there is a difference between the two diet groups in the proportions of women who developed breast cancer.
3. Calculate the sample proportion, pL(^ symbol on top) , of women on the low-fat diet who later developed breast cancer, and calculate the sample proportion, pN(^ symbol on top), of women on the normal fat diet who later developed breast cancer.
4. Calculate the sample difference in proportions, pL-pN .
5. Calculate the pooled proportion, p(line on top) , of women who developed breast cancer.
6. Calculate the standard error, σ, of the sampling distribution for differences in sample proportions.
7. Calculate the z-score for your sample difference in part d., and use normalcdf() to calculate the p-value for this sample difference.
8. Using a significance level of 1% = 0.01, should we reject or fail to reject the null hypothesis?
9. Write your conclusion from part h. in a way that a non-statistics person would understand

Answer 1