Question

Find the probability of a Type I error.

A) 1/5 B) 0.4 C) 0.5​ D) 0.6 E) 0.7.

There are 5 black, 3 white, and 4 yellow balls in a box (see picture below). Four balls are randomly selected with replacement. Let M be the number of black balls selected. Find P[M =2].

A) Less than 10%

B) Between 10% and 30%

C) Between 30% and 43%

D) Between 43% and 60%

E) Bigger than 60%.

Use the following information to answer Q19 and Q20:

You must decide which of two discrete distributions a random variable X has. We will call the distributions p0 and p1. Here are the probabilities they assign to the values x of X:

x

0

1

2

3

4

5

6

p0

0.05

0.05

0.0

0.1

0.3

0.1

0.4

p1

0.2

0.0

0.2

0.2

0.2

0.1

0.1

You have a single observation on X and wish to test

​H0: P0 is correct

​Ha: p1 is correct

One possible decision procedure is to reject H0 if X ≥ 5 and retain H0 otherwise.

Answer 1

Total number of balls is 5+3+4=12

Number of ways 4 can be drawn is

As we are looking for 2 black balls, there are 5 black balls and 3+4=7 non black balls
Hence number of ways in which 2 black and 2 non black balls are drawn is

So the probability is

Option C is correct.

2) Since Type-I is probability of rejecting a true null hypothesis,

If H0 is true than P0 is correct

And we reject H0 if so we have

Probability of Type-1 error is 0.1+0.4=0.5

Option C is correct.