Dicey Discussion William Gray.docx (1)

STA 215 Name: William Gray We should expect a population parameter to be close to the corresponding statistic when we only take a sample, and vice versa. This will work for means (we would expect the mean height of all GVSU students to be close to the mean height of our classes) or for proportions (we should expect to roll a 6 around 1/6 of the total times we roll it). If we know p (population proportion) we will see that (sample proportion) follows a normal 𝑝 ^ distribution with the following: mean (center)= p standard deviation (spread)= 𝑝(1 − 𝑝)/𝑛 Suppose I have a die, and I want to consider even numbers to be successes and odd numbers to be failures. What do we expect p (the proportion of successes) to be based on the long-run relative frequency interpretation of probability? p= 3/6, 50%, 1/2 1. What should we expect the center and the spread to be for the distributions of for each of ρ ^ parts A, B, and C? (We know p and n . That should be all you need to know. This is NOT based off your individual data.) Mean of values ρ ^ S.D. of values ρ ^ n = 5 0.5 0.2236 n = 10 0.5 0.1581 n = 20 0.5 0.118 2. For each sample size, calculate the mean and the standard deviation of the sample proportions. Mean of values ρ ^ S.D. of values ρ ^ n = 5 0.500 0.219 n = 10 0.506 0.157 n = 20 0.504 0.123 3. Are the means of the sample proportions for n = 5, 10, and 20 roughly equal to p ? They are roughly close. 4. What happens to the spread of the sampling distribution of as the sample size increases? ρ ^ The spread of the sampling size decreases as the sample size increases.