Question

What are the conditions required for conducting a one- sample proportion z- test?

Answer 1

Hint: To solve this question we need to have the concept of Z-test. So basically this test is a statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution. A normal distribution is a type of continuous probability distribution for a real valued random variable.

Complete step-by-step answer:
The question asks us to give the conditions which are required for the conduction of one sample proportion Z-test. So for knowing the conditions the first step will be to look at the explanation of one sample z-test.
Z-test is a statistical test to determine whether two population means are different when the variances are known and the sample size is large. It can be used to test hypotheses in which the z-test follows a normal distribution. A z-statistic, or z-score, is a number representing the result from the z-test.
Assumptions of the one sample Z Proportion test are:
(i)The data are simple random values from the population of the interest.
(ii)Population follows a binomial distribution
(iii)When both mean $np$ and variance $n.\left( 1-p \right)$ values are greater than $10$, where $n$ and $p$ are sample size and the true population proportion respectively, the binomial distribution can be approximated by the normal distribution

Note: Z-tests are statistical calculations that can be used to compare population means to a sample's while when we talk of T-tests, it is basically used for the calculations to test a hypothesis, but it is most useful for the determination of its statistical significant difference between two independent sample groups.