1 Twenty students are eligible for a GTLD program in my scho

1. Twenty students are eligible for a GT/LD program in my school district. A simple random sample of five is selected.

A. How many different random sample selections are possible?

B. What is the probability of each simple random sample?

2. You choose an alpha level of .01 and then analyze your data.

a. What is the probability that you will make a Type I error given that the null hypothesis is true?

b. What is the probability that you will make a Type I error given that the null hypothesis is false?

Please show all work. Thanks.

Solution

Q1.
a) To find the number of possible ways in which we can select five students, out of twenty is = 20 C 5
= nCr(20,5)= (20!)/(5! *15!) = 15504
  
b) Probability of picking of each simple random sample = 1/15,504 = 0.0000645