type 1 and 2 errors Flashcards
The sum of the values of alpha and beta
need to find out
What type of error occurs if you fail to reject H0 when, in fact, it is not true?
Type II
The probability of committing a Type I error when the null hypothesis is true is
The level of significance
In hypothesis tests, the smaller the type I error, the _______the type 2 error
the larger the type 2 error
THe level significance is (relating to type I and II errors)
maximum allowable probability of Type I error
the power curve provides the probability of
correctly rejecting the null hypothesis
Type 2 error is committed when
a true alternative hypothesis is mistakenly rejected
the error of rejecting a true null hypothesis is
a type 1 error
The level of significance in hypothesis testing is the probability of
rejecting a true null hypothesis
In hypothesis testing if the null hypothesis has been rejected when the alternative hypothesis has been true,
the correct decision has been made
The probability of making a Type I error is denoted by
alpha
The probability of making a Type II error is denoted by
Bata
If a hypothesis test leads to the rejection of the null hypothesis,
a Type I error may have been committed
If the probability of a Type I error (a) is 0.05, then the probability of a Type II error (B) must be
need to figure out
If the level of significance of a hypothesis test is raised from .01 to .05, the probability of a Type II error
will decrease
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.
A Type II error has not been committed since H0 was rejected.
What is a type I error
the prob of rejecting a true H0
What is the prob of committing a type I error
it is just a significance level -a
What are some common choices for the significance level
0.05 and 0.01
What does the significance level control
the prob of making a type I error
if the cost of making a type I error is not too high, then what can you use for a?
larger value of a are typically used
what does a significance test control
only controls type I error
- most applications only control type I errors
because of the uncertainty associated with making type II errors, what should we say
“Do not reject Ho” instead of “Accept Ho”
whenever the prob of making Type II error has NOT been determined and controlled use
Do Not Reject HO or
Reject HO
Is controlling type 2 errors common
no
If proper controls have been established for TYpe II errors it can be appropriate to say
Accept HO
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
Step1: conduct the hype test (test his claim)
Ha: M< 60%
n = 51, M = .60, Xbar = .57, Q .12, a = 0.01
- Convert to standard normal distribution (z-Value)
= -2.33 - Solve for CV for original
CV = M+Z (SE) = 56.08 - Draw test distribution (reject / fail to reject regions and Ha being the mean and CV = 56.08
- 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%
