Q1.  I created a function to do the calculations to find mu for the Confidence Interval:

ci <- function(xbar, con, sig, n)
{
con1 = con + ((1-con)/2)
mu = xbar + (qnorm(con1) * (sig / sqrt(n)))
sn = xbar – (qnorm(con1) * (sig / sqrt(n)))
paste(“The confidence interval is between “, sn, ” and “, +mu, ” and the estimated mean is “, xbar, sep =””)
}

The confidence intervals came in as follows:

> ci(115, .9, 15, 100)
[1] “The confidence interval is between 112.532719559573 and 117.467280440427 and the estimated mean is 115”
> ci(115, .95, 15, 100)
[1] “The confidence interval is between 112.06005402319 and 117.93994597681 and the estimated mean is 115”
> ci(115, .98, 15, 100)
[1] “The confidence interval is between 111.510478188939 and 118.489521811061 and the estimated mean is 115”

Q2

[1] “The confidence interval is between 83.0400360154599 and 86.9599639845401 and the estimated mean is 85”

Q3

((1.96 * 15) / 5)^2
[1] 34.5744

I think the minimum sample size should be 35 if I’m thinking of the zscore tails properly.

edit: After reviewing the last question, 35 is right, but how i got to it was wrong

III

The biggest thing to note about this is the difference between the 95% confidence interval and the 97.5th percentile ranking.  Each tail of the 95% confidence interval contains 2.5% of the area under the curve.  But we’re only looking for a single tailed value, so we must use qnorm(.975).

I feel like I was perhaps a little bit confused about what questions 1 and 2 were asking for, or what the answer should look like.