Distribution of Sample Proportions

Front

What is the definition of sample proportion (p-hat)?

Back

The sample proportion (p-hat) is the ratio of the number of successes in a sample to the total number of observations in that sample.

Front

What are the conditions for the sampling distribution of p-hat to be approximately normal?

Back

1. The sample is drawn randomly from the population. 2. The sample size is large enough such that both np ≥ 10 and n(1-p) ≥ 10.

Front

If a population has a proportion of 49% males, what is the value of p?

Back

p = 0.49

Front

What is the formula for the standard error of the sample proportion?

Back

Front

What does it mean if the sample size is too small to consider the distribution of p-hat normal?

Back

It means that the sample size does not meet the conditions np ≥ 10 and n(1-p) ≥ 10, which are necessary for the Central Limit Theorem to apply.

Front

How do you calculate the probability of a sample proportion falling within a certain range?

Back

You can use the normal approximation to the binomial distribution, calculating the z-scores for the sample proportions and using the standard normal distribution to find probabilities.

Front

What is the significance of the Central Limit Theorem in relation to sample proportions?

Back

The Central Limit Theorem states that the distribution of sample proportions will be approximately normal if the sample size is sufficiently large, regardless of the population distribution.

Front

What is the difference between p and p-hat?

Back

p is the true population proportion, while p-hat is the sample proportion calculated from a specific sample.

Front

What is the probability of obtaining a sample proportion less than a certain value when the distribution is normal?

Back

To find this probability, calculate the z-score for the sample proportion and use the standard normal distribution table to find the corresponding probability.

Front

What is the formula for calculating the z-score for a sample proportion?

Back