Which of the following criteria must be met to do a one-proportion z- test?

A. The data values in the sample must be dependent.
B. The parent population must be normally distributed.
C. The data must come from a random sample.
D. The sample size must be more than 10% of the population size.
E. The sample size must be less than 10% of the population size.
F. You must expect at least 10 "successes" and at least 10 "failures", that is np ≥ 10 and nq ≥ 10
G. The data values in the sample must be independent.


A) A, B, C, F
B) A, C, D, F
C) B, D, F, G
D) C, D, F, G
E) C, E, F, G

I'm leaning towards D as the answer...would I be correct?

Looks OK!

To determine which criteria must be met for a one-proportion z-test, let's go through each option:

A. The data values in the sample must be dependent.
This statement is not correct. For a one-proportion z-test, the data values in the sample must be independent, as option G suggests. Therefore, A is incorrect.

B. The parent population must be normally distributed.
The normality assumption applies to the sampling distribution of the sample proportion, not the parent population. So, B is incorrect.

C. The data must come from a random sample.
Random sampling is necessary for generalization of the results to the population. This is a correct criterion for a one-proportion z-test.

D. The sample size must be more than 10% of the population size.
The 10% requirement applies to the sample size relative to the population size for the Central Limit Theorem to hold. So, D is incorrect.

E. The sample size must be less than 10% of the population size.
This option also relates to the 10% requirement, but it is the opposite of what is needed. So, E is incorrect.

F. You must expect at least 10 "successes" and at least 10 "failures", i.e., np ≥ 10 and nq ≥ 10.
This statement refers to the minimum expected counts for the sample size used in the test. The presence of at least 10 successes and 10 failures ensures that the normal approximation is appropriate. Therefore, F is a correct criterion for a one-proportion z-test.

G. The data values in the sample must be independent.
Independence of the data values is crucial for conducting hypothesis tests. It ensures that each observation is not influenced by other observations from the sample. This is a correct criterion for a one-proportion z-test.

Based on the above analysis, the correct answer is D) C, D, F, G.