In a large experiment to determine the success of a new drug, 500 patients with a certain disease were given the drug. If more than 340 but less than 385 patients recover, the drug is considered 73% effective.

a) Find the level of significance of this test

b) If the drug is 76% effective, find the probability of the type II error

I don't know what to do with the range of numbers. I am assuming I need to subtract everything up to 340 off of everything up to 385, but I can't figure it out. I have no idea about part b.

In a process, it is found that a sample of size 100 yields 12 defective parts.

a) How large a sample is needed if we wish to be 98% confident that our sample proportion will be within 0.05 of the true proportion defective?

b) By how much must the sample size n be increased to halve the width of a confidence interval?

I don't know what we are comparing it to. Only the sample was given.

On the basis of extensive tests, the yield point of steel-reinforcing bar is known to be normally distributed with standard devitation of 100.

a) If a sample of 25 bars resulted in a sample average yield point of 8439 lb, compute a 90% CI for the true average yield point of the bars.

b) How would you modify the interval in part a) to obtain a confidence level of 92%?

I hate CIs...it's the stuff I missed.

A researcher claims that the life span of mice can be extended by 25% when the calories in their food are reduced by 40% from the time they are weaned. Suppose a sample of 27 mice yield a sample mean of 21 mo and s=3.2. Test to see if sigma really is 5.8 when alpha is 0.05.

I don't really get this one either. I wrote some stuff down, but all I end up doing is stopping with no real information found.

The recommended daily dietary allowance for zinc among males older than age 50 is 15 mg/day. A sample of 124 males who are older than 50 gave an average intake of 11.3 mg/day and a standard deviation of 6.43 mg/day. Does this data indicate that the average daily intake in the population of over 50 males falls below the recommended allowance?

...?...

Let X1, X2, ... , Xn be iid U(0, theta).

a) Find the maximum likelihood estimator of theta

b) Find the cumulative distribution function of theta = max(Xi)

c) Find the pdf of Theta

d) Compute E(theta)

e) Find a (1-alpha)100% confidence interval for theta

f) For what values of k is k times Theta unbiases?

I'm not even sure what U is

Let S= sqrt((summation i=1 to n of (Xi - Xbar)^2)/n-1) be the sample of standard deviation for a random sample from a normal population, find the E(s).

The trick to this one is alledgedly doing it in parts, but I don't even know what part 1 is.