8.2: The Sampling distribution of the sample proportion Flashcards
What is the sampling distribution of the sample proportion?
The sampling distribution of the sample proportion is the probability distribution of all possible values of the sample proportion p̂ from different possible samples of the same size from the population.
What does the sample proportion p̂ represent?
The sample proportion p̂ represents the point estimate of the population proportion p.
When can the sampling distribution of p̂ be approximated as normally distributed?
The sampling distribution of p̂ can be approximated as normally distributed if the sample size n is large. Specifically, n should be large enough that both np and n(1 - p) are at least 5.
What is the mean (μp̂) of the sampling distribution of the sample proportion p̂?
The mean (μp̂) of the sampling distribution of the sample proportion p̂ is equal to the true population proportion p.
How is the standard deviation (σp̂) of the sampling distribution of p̂ calculated?
The standard deviation (σp̂) of the sampling distribution of the sample proportion p̂ is calculated as the square root of [p(1 - p) / n].
What is the condition under which the standard deviation formula for the sampling distribution of p̂ is exact?
The standard deviation formula for the sampling distribution of p̂ is exact if the population is infinite and is approximately correct for finite populations that are much larger than the sample size.
Why is it important for the np and n(1 - p) to be at least 5 when using the normal approximation for the sampling distribution of p̂?
The requirement that np and n(1 - p) are at least 5 ensures that the sampling distribution of p̂ will not be significantly skewed, which allows for the normal approximation to be more accurate.
