Question

We want to test the null hypothesis that a certain diamond is selling around the country for an average price of $523 against the alterna-tive hypothesis that the diamond is not selling for this average price. We take a random sample of 100 jewelry stores and decide to reject the null hypothesis if our sample average is less than $515 or more than $531. We can assume that our standard deviation is $42.
a. What is the probability of a Type I error?
b. What is the probability of a Type II error if in
reality the average price of the diamond is $532?

Answer 1

I know how to solve it, but unsure whether to use t or z tests.

Answer 2

if population sigma is known, z test, otherwise t test

Answer 3

its hard to tell if the standard deviation is refering to the sample or population. but since its not specifically stated as the sd of the sample its a pretty fair bet that its the pop sd

Answer 4

we used to have a n<30 assumption but there have been classes lately that say that is an old process.

Answer 5

ok, now the problem you posted is not asking for a z/t test. its asking for type of errors.

one type of error is that the null is true and we reject it
the other type of error is that the null is false and we fail to reject it

which is which should be more comprehendable from your own literature.

Answer 6

Alright, thanks.

Answer 7

so yeah, you might need to know the test statistic in order to determine the probability of error .... sometimes i have to read these things a few times :)

Answer 8

heres a better picture that demonstartes the errors

type 1 is an alpha error, alpha being the rejection region. its rejecting a true null

type 2 is a beta error, its related to the rejection region of the sample/alternative hypot. its the error of failing to reject a false null.