# 7 Statistics Problems I Cannot Solve

#### sjaguar13

I was sick recently, and missed two days of class. Out of 35 problems, I got stuck on these 7:

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.

#### JasonRox

##### ... to graduate school.
Homework Helper
Gold Member
sjaguar13 said:
I was sick recently, and missed two days of class. Out of 35 problems, I got stuck on these 7:

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.
Are you sure you even tried these exercises?

I haven't been in a Stats in a few years now, and remember just about nothing. By reading your questions, I remember the similarity with the questions I used to do. The best thing to do is go to class so the prof walks you through examples, and then when homework comes, follow the example the prof gave you with the problem you are working on.

For example, this question...

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.
I'm pretty positive that is enough information. There is nothing to compare it to, so I'm not sure what you are talking to.

I might sound rude for asking this, but did you go to class?

#### JasonRox

##### ... to graduate school.
Homework Helper
Gold Member
Oh, and I can't help because I don't really remember anything.

My advice is just to follow other examples as you do your exercises. That worked well for me.

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