SOLVED: quuestion 8 Find the 95% confidence interval for the population proportion, p, when n = 28 and x = 12. Use your calculator memory function to store the p-hat value, or use 5 or 6 places of dec

quuestion 8
Find the 95% confidence interval for
the population
proportion, p, when n =
28 and x = 12. Use your calculator
memory function to store the p-hat value, or use 5 or
6 places of decimal if you are entering the p-hat
value in the formula. Enter only the LOWER boundary of
your interval as your answer, rounded to 3 places of
decimal.
CAUTION: A very common error in this question is to think
because n = 28 that we will be using
the t-distribution. This is NOT the case. We ONLY use
the t-distribution when we are dealing with means.
And it is true that IF we were dealing with
means and n = 28 and the underlying
population was normally distributed, then we would be using
the t-distribution.
But in this question we are dealing
with proportion, and the question we must ask
ourselves
is not “is n thirty
or more?”, but: “are we expecting at least 5 successes and at least
5 failures?”
Question 9
In the situation considered in question 8, what size sample
would be necessary to find, with 95% confidence, the true
proportion, p, to within 5%?
You may wish to use your memory function to store
the p-hat value, or use 5 or more places of decimal
until you round your final answer.

1.) If n=460 and (p-hat) =0.43, find the margin of error at a
90% confidence level
Give your answer to three decimals
B.) Assume that a sample is used to estimate a population
proportion p. Find the 99.5% confidence interval for
a sample of size 108 with 21 successes. Enter your answer as a
tri-linear inequality using decimals (not percents) accurate to
three decimal places.
_____ < p < ________
Answer should be obtained without any preliminary rounding.
However, the critical value may be rounded to 3 decimal places.