A group of students wants to research whether a higher education degree will yield more job opportunities. They created two fake resumes and the only difference between them was their name and the level of education. One is a high school graduate and the other is a college graduate. Their experiment results are as follows: The high school graduate got 127 from 1200 views and the college graduate got 150 offers from 1050 views.

a). Without solving the problem, take a guess that whether the college graduate or the high school graduate has the higher proportion of job offerings.

b). Using the data above, find a 90% confidence interval for the difference in offer proportion for those two resumes. (college - high school)

c). What will happen if we change the confidence interval in part b to 40%? Will the confidence interval be narrower or wider?

d). Using the R code to solve the problem in part b. The answer should be the same as part b.

e). Can you draw the conclusion that a higher degree can certainly provide more job opportunities from this experiment?