10.4: z tests about population Proportion Flashcards
What is the purpose of a z-test for a population proportion?
A z-test for a population proportion is used to determine if there is a significant difference between the sample proportion and a claimed population proportion.
When can you use a z-test for a population proportion?
A z-test can be used when the sample size is large, typically n ≥ 30, which ensures that the sampling distribution of the sample proportion is approximately normally distributed.
What is the null hypothesis for a z-test about a population proportion?
The null hypothesis (H₀) for a z-test about a population proportion is that the population proportion (p) is equal to a hypothesized value (p₀), written as H₀: p = p₀.
What is the test statistic formula for a z-test about a population proportion?
The test statistic for a z-test is z = (p̂ - p₀) / √[p₀(1 - p₀) / n], where p̂ is the sample proportion, p₀ is the hypothesized population proportion, and n is the sample size.
What are the assumptions for conducting a z-test for a population proportion?
The assumptions are that np₀ ≥ 5 and n(1 - p₀) ≥ 5, which ensure that the sample size is adequate for the approximation to the normal distribution to be valid.
How do you interpret the critical value rule in a z-test for a population proportion?
If the calculated z value is greater than the critical value (zα) for a one-tailed test, or the absolute value of z is greater than the critical value for a two-tailed test, reject H₀.
What does a p-value represent in a z-test for a population proportion?
The p-value represents the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed if the null hypothesis is true.
What does it mean if a z-test yields a p-value of 0.0005?
A p-value of 0.0005 indicates very strong evidence against the null hypothesis, suggesting that it is very unlikely that the observed sample proportion is due to random chance if the null hypothesis were true.
