In a study, two groups of randomly chosen patients with a particular infection are given either oral treatment or treatment by injection. Out of the 100 patients who took the oral treatment, 28 cured within 4 days. Whereas 32 out of 91 patients who took the treatment by injection cured within 4 days. The 90% confidence interval of the difference between proportion of cured patients who took treatment by injection and that of cured patients who took oral treatment within 4 days is calculated to be(-0.039, 0.182). Assume that all conditions for calculating a meaningful confidence interval are satisfied, which of the following statements are correct?

Select one or more:

a.There is a 90% chance that the true difference between the proportion of cured patients who took treatment by injection and that of cured patients who took oral treatment within 4 days is between -0.039 and 0.182.

b.Based on the confidence interval, we would fail to reject the null hypothesis that there is no differencein the proportion of patients cured between those that use the treatment by injection and those that use the oral treatment, thus there is not sufficient evidence in favor of the two-sided alternative at an=0.05

level.

c.We are 90% confident that the true difference between the proportion of cured patients who took treatment by injection and that of cured patients who took oral treatment within 4 days is between -0.039 and 0.182.

d.We are 90% confident that the difference between the sample proportion of cured patients who took treatment by injection and that of cured patients who took oral treatment within 4 days is between -0.039 and 0.182.

e.Based on this confidence interval, we would reject the null hypothesis that there is no difference in the proportion of patients cured between those that use the treatment by injection and those that use the oral treatment in favor of the two-sided alternative that there is a difference at an=0.1

level.