How Do I Solve These Statistics Final Exam Questions?

[Red98Stang]

I'm currently studying for a Statistics final, and I'm stuck at some problems. I'd appreciate any help I could get.

Question #1

Determine the minimum sample size needed to estimate a population mean with a margin of error of 24 and a confidence level of 95%, if the population standard deviation is 234.

n = ?

Question #2

Professors seem to believe that students score better on exams on Tuesdays, Wednesdays, and Thursdays than on Mondays or Fridays. A sample of the number of A and B grades achieved by a class on various days, Monday through Friday, is 15, 18, 17, 22, 16. A test is made of the claim, at a significance level of 0.05, that A and B grades occur with equal frquency on all days.

What is the test statistic?

What is the critical value?

 

[HallsofIvy]

The first just requires that you use the standard formula,
$$z= \frac{x-\mu}{\sqrt{n\sigma}}$$
Here that is
$$z= \frac{24}{\sqrt{234n}}$$
Using a table of the standard normal distribution, what z corresponds to a (two-sided) value of 0.95? Put that into the equation above and solve for n.

The second problem really just about definitions. The "test statistic" is difference between the average score on Monday and Friday and the average score the other days. The critical value is the value of that test statistic that would be on the boundary of a 95% interval.

 

[mattmns]

What level class is this for?

Because I would think you would want to use the following formula for the first question:

$$n = \left(\frac{z \sigma}{ME}\right)^2$$

Where z is your z* or z alpha/2, or whatever it is that your class/book uses, sigma is your population standard deviation, and ME is your margin of error.

 

[Red98Stang]

Thanks for all the help so far. It's an Intro to Statistics class at my college.