type 1 and 2 errors

Question 1

The sum of the values of alpha and beta

Answer 1

need to find out

Question 2

What type of error occurs if you fail to reject H0 when, in fact, it is not true?

Answer 2

Type II

Question 3

The probability of committing a Type I error when the null hypothesis is true is

Answer 3

The level of significance

Question 4

In hypothesis tests, the smaller the type I error, the _______the type 2 error

Answer 4

the larger the type 2 error

Question 5

THe level significance is (relating to type I and II errors)

Answer 5

maximum allowable probability of Type I error

Question 6

the power curve provides the probability of

Answer 6

correctly rejecting the null hypothesis

Question 7

Type 2 error is committed when

Answer 7

a true alternative hypothesis is mistakenly rejected

Question 8

the error of rejecting a true null hypothesis is

Answer 8

a type 1 error

Question 9

The level of significance in hypothesis testing is the probability of

Answer 9

rejecting a true null hypothesis

Question 10

In hypothesis testing if the null hypothesis has been rejected when the alternative hypothesis has been true,

Answer 10

the correct decision has been made

Question 11

The probability of making a Type I error is denoted by

Answer 11

alpha

Question 12

The probability of making a Type II error is denoted by

Answer 12

Bata

Question 13

If a hypothesis test leads to the rejection of the null hypothesis,

Answer 13

a Type I error may have been committed

Question 14

If the probability of a Type I error (a) is 0.05, then the probability of a Type II error (B) must be

Answer 14

need to figure out

Question 15

If the level of significance of a hypothesis test is raised from .01 to .05, the probability of a Type II error

Answer 15

will decrease

Question 16

A sample of 30 cookies is taken to test the claim that each cookie contains at least 9 chocolate chips. The average number of chocolate chips per cookie in the sample was 7.8 with a standard deviation of 3.

Compute the probability of a Type II error if the true number of chocolate chips per cookie is 8.

Answer 16

A Type II error has not been committed since H0 was rejected.

Question 17

What is a type I error

Answer 17

the prob of rejecting a true H0

Question 18

What is the prob of committing a type I error

Answer 18

it is just a significance level -a

Question 19

What are some common choices for the significance level

Answer 19

0.05 and 0.01

Question 20

What does the significance level control

Answer 20

the prob of making a type I error

Question 21

if the cost of making a type I error is not too high, then what can you use for a?

Answer 21

larger value of a are typically used

Question 22

what does a significance test control

Answer 22

only controls type I error

• most applications only control type I errors

Question 23

because of the uncertainty associated with making type II errors, what should we say

Answer 23

“Do not reject Ho” instead of “Accept Ho”

Question 24

whenever the prob of making Type II error has NOT been determined and controlled use

Answer 24

Do Not Reject HO or

Reject HO

Question 25

Is controlling type 2 errors common

Answer 25

no

Question 26

If proper controls have been established for TYpe II errors it can be appropriate to say

Answer 26

Accept HO

Question 27

Peter claims the avg score for the final exam is less than 60%. You gather a sample of 51 test papers and calculate the sample avg to be 57% and pop sd to be 12%.

Suppose the teacher knows the true avg is 58%

Calculate the prob of Type II error with a claim at the 1% significance level

Answer 27

Step1: conduct the hype test (test his claim)
Ha: M< 60%

n = 51, M = .60, Xbar = .57, Q .12, a = 0.01

2. Convert to standard normal distribution (z-Value)
   = -2.33
3. Solve for CV for original
   CV = M+Z (SE) = 56.08
4. Draw test distribution (reject / fail to reject regions and Ha being the mean and CV = 56.08
5. calculate type 2 error
   x- m/ se

56.08 - 58 / 12/ square root 51
= -1.14
area = 0.12714
we want the area to the right so 1 - 0.12714 = 0.87286

Therefore, the prob of making a type 2 error is 87.286%