# Parameter vs. Statistic # Sampling Distribution

• The "sampling distribution" is the values taken by the statistic in all possible samples of the same size from that population

• The "sampling distribution" is always referring to the distribution of the sample # Central Limit Theorem

• The sampling distribution of the sample mean is normally distributed  # Conditions (RIN)

• Random

• How the sample is selected
• Independent

• N≥10n

• N: population size

• n: sample size

• Normal

• For means

• • If the population is normally distributed, n can < 30

• For proportions:

• # Sampling Distribution of a Sample Mean

• • # Sampling Distribution of a Sample Proportion

• # Review # Practice Questions

1. Assume graph X represents the actual distribution select which graph the sampling distribution of the sample mean look like, for a sample size of n = 50? 1. The weight of the eggs produced by a certain species of chicken is Normally distributed with mean 65 g and standard deviation 5 g.
• If a farmer selects a random sample of 10 every morning to check the health of his laying hens, what is the mean and SD of the sampling distribution of the weight of the eggs? • Calculate the probability that a randomly selected egg weighs between 61g and 69g • Calculate the probability that the mean weight of the farmers 10 eggs falls between 61g and 69g.  1. A survey asks a random sample of 500 adults in California if they support an increase in the state sales tax of 1%. Suppose that 40% of all adults in California support the increase.
• If p hat is the proportion of the sample who are in favor of the increase, what is the mean of the sampling distribution of p hat? The SD?  • How large a sample would be needed to guarantee that the standard deviation of it is no more than 0.02?  • Find the probability that p hat is between 0.36 and 0.42 