3 statistical method questions

soshi367

1.) When I played baseball (from age 8 through high school), I had an overall batting average of .325 (meaning I got a hit 325 out of every 1000 at bats).
a) If I were to have 4 at bats in a particular game, what is the probability that I had at least 1 hit?
b) If I were to have 300 at bats in one season, what is the probability that I had at least 120 hits?

2.) A study of 74 patients with ulcers was conducted in which they were prescribed 40mg of Pepcid. After 8 weeks, 58 patients reported ulcer healing. With 95% confidence, is there enough evidence to indicate that the percentage of patients that reported ulcer healing after using Pepcid above 70%? Why or why not?

3.) Last year, the average overall score in my College Algebra classes was 72.5 with a standard deviation of 7.5 and the scores were distributed normally.
a) If the top 9% of scores were to earn A grades, what score would separate A grades from the rest?
b) What is the probability that the average overall score of 10 randomly selected tests is above 90.0?
Would this be considered unusual? Why or why not?

Hey guys my final in this class is coming up and out of about 50 questions these seem to be giving me the most trouble. what kind of equations would i use? any help at all would be appreciated.

adam

yeah I would go to somethingawful with this. Too much to handle here.

Aldo

I'm not going to answer those questions for you, I always had problems with these questions as well. What is important is that you sit back and write down what you know and what is asked of you, if we take question 2 for example you know the following:

78,38% of the patients reported healing, they ask if that means that you can be 95% sure that the medicine heals at least 70% of all patients. So you know that in this case more than 70% of the patients reported healing, but can you extrapolate those results to the complete population?

The next step is to figure out what test you must conduct to find that out. You know the following: it's a statistical test because n>30, you are dealing with 1 case (patients with ulcers) and there's only 2 options: a patient gets healed or he doesn't.

So if I didn't royally fuck up somewhere along the line this means you gotta go for a Z-test on H0: Pu=a.

If you really need help you're better off asking your teacher in person, as he can explain it much better than people on a forum.

GoodOmens

For question 1, you'll use binomial distribution. That's one's very straightforward, you have the probability of success (I'm assuming that the .325 is a constant probability, which isn't really accurate, but whatever), number of attempts, and you want a certain number of successes.

For part A, it would be easier to simply find the probability of 0 successes, and subtract that from 1. For part B, because the numbers are bigger, you might consider using the Poisson approximation (make sure you check if that's allowed).

Question 2, like Aldo said, hypothesis test.

Question 3, part A you want inverse normal distribution. Part B, use the Central Limit Theorem.

|I didn't include the equations because, well, they're a giant pain and you have a textbook anyway.

Hope that helps. I can give you more information if you get stuck again. These look like exactly the type of questions I give my students.

Gdiguy

soshi367 wrote: »

1.) When I played baseball (from age 8 through high school), I had an overall batting average of .325 (meaning I got a hit 325 out of every 1000 at bats).
a) If I were to have 4 at bats in a particular game, what is the probability that I had at least 1 hit?
b) If I were to have 300 at bats in one season, what is the probability that I had at least 120 hits?

For a & b, they're basically the two ways to calculate P(X >= c); either you can reform it in a way that gets rid of the > sign (a), or you have to use some sort of cumulative distribution function (b)

a) The simpler way - remember that P(A happening) = 1 - P(not A happening). So P(# hits >=1) = 1 - P (# hits not >=1) = 1 - P(# hits = 0). For some probability p of getting a hit in a single at bat, the probability of not getting a hit 4 times in a row is just p^4

b) As the previous post says, you need to use the c.d.f. function; I would be very wary of using Poisson here (you should be using a Poisson estimate for rare events, and 120/300 isn't really rare)... calculating it exactly with binomial is pretty impossible by hand for this (though it's like a 3 line perl script), but usually for something like this you want the Normal (Gaussian) approximation, which is to treat the events instead of as binomial (p) but as normal with mean np and variance np(1-p)... then calculating it is easier

other two parts were answered better than i can at 5:30 in the morning