Central Limit Theorem Conditions for ro ortions: 0 Condition 1: The sample we have taken is random and independent. 0 Condition 2: The sample size, n, is large enough to expect at least 10 successes and 10 failures. - Condition 3: The populations is at least 10 times the sample size. N 2 107:. If we take a sample and all of the above conditions hold, then the distribution of the sample proportion is normal with a mean equal to the population proprtion (or sample proportion if we don't know it) and a standard deviation equal to the standard error (or standard error estimate). Variables: p = the proportion of the population who ts in the group we care about (not always known) p" = the proportion of our sample who ts in the group we care about Standard Error Calculations (1 ) 30 P 5593: = n 1: SE = 2. Suppose we flip a coin, and we are interested in the proportion of the time that the coin comes up heads. A) Suppose we ip the coin 100 times. Does this satisfy the 3 conditions of CLT? If so, draw the sampling distribution below. B} What is the probability of nding a sample that has a proportion of heads that is higher than 60%? C} Suppose we ip the coin 200 times. Draw the sample distribution below. What is the difference between our distributions in A and C? D) What is the probability of nding a sample that has a proportion of heads that is higher than 60%