1. ## Confidence Intervals

Need help with these questions please:

1. The mean wing span of a random sample of 35 birds is 186mm and the standard deviation is 28mm. Give the upper limit of a 90% confidence interval for the population mean wing span of birds, calculate using large-sanple methods.

2. An approximate 95% confidence interval for some population parameter $\mu$ > 0 is (1.77, 2.15). The parameter $\theta$ is obtained from $\mu$ by the transformation of $\theta$=10/2 $\mu$+1. Give the lower confidence limit of an approxiamate 95% confidence interval for $\theta$.

3. In an opinion poll, 720 people are interviewed; 458 answer Yes to a particular question, and the remaining 262 answer No. An approximate 99% confidence interval is calculated for the underlying probability of answering Yes. Give the lower limit of this interval.

4. In a trial of a new drug against newly-diagonised rheumatoid arthritis, 130 patients are randomly assigned to the new drug and 128 to the standard treatment. After a period of time, 84 of those assigned to the new drug and 65 of those assigned to the standard treatment are found to have improved. Give the upper confidence limit of a 95% confidence interval for the difference between the underlying proportion of patients on the new drug whose condition improves and the underlying proportion of patients on the standard treatment whose condition improves.

See post below for options

2. These questions aren't that clear to me.
Are they talking about one-sided confidence intervals
OR the end points of a two-sided interval?
MY guess is the later, but at first I felt that these questions pertained to one-sided intervals.

IN 1. The mean wing span of a random sample of 35 birds is 186mm and the standard deviation is 28mm. Give the upper limit of a 90% confidence interval for the population mean wing span of birds, calculate using large-sanple methods.

you would calculate $186+z_{.05}28/\sqrt{35}$.

BUT if you're asking about a one-sided CI, we would obtain $186+z_{.10}28/\sqrt{35}$.

OK, in 2, my problem is figuring what is meant by $=10/2\mu$+1, I would like to see ().

This could be $5\mu$+1 OR $(5/\mu)$+1 OR $10/(2\mu+1)$.

IN any case you solve for $\theta$.

IN 3, I'm guessing that you're asking for the lower value in a 2 sided interval $\hat p-z_{.005}\sqrt{\hat p\hat q/n}$