An article in Fortune (September 21, 1992) claimed that one-half of all engineers continue academic studies beyond the B

[answerhappygod]

An article in Fortune (September 21, 1992) claimed that one-half
of all engineers continue academic studies beyond the B.S.
degree, ultimately receiving either an M.S. or a Ph.D. degree. Data
from an article in Engineering Horizons (Spring 1990)
indicated that 117 of 484 new engineering graduates were planning
graduate study. Are the data from Engineering Horizons
consistent with the claim reported by Fortune? Test the hypothesis
at α = 0.05.
6). Discuss how you could have concluded the test by
constructing a confidence interval on the parameter of
interest.
7). What is the the type II error probability β for the test
that uses n = 484 and α = 0.05 when the true proportion of
engineering students planning graduate studies was 53%?
8). Based on the data set and setup of the test, do you think
Engineering Horizons would commit the type II error? Why?

9). Suppose that Engineering Horizons was willing to accept a
β-error as large as 0.10 if the true proportion of
engineering
students planning graduate studies was 53%. At α = 0.05, what
sample size would be required?