Question

A. Suppose you take a sample of size n from a population and calculate a statistic from that sample. The statistic could be a sample proportion p, a sample mean x, or another statistic. Then suppose we repeat this process over and over again until we find all possible samples of size n from the population (this is a theoretical idea) and we calculate the same statistic from 1. each sample. The collection of all of the statistics calculated is called the for that statistic. B. Suppose we carry out the above scenario with the sample proportion p from a population with population proportion p. Then the mean of all of the sample proportions is C. The standard deviation of the sample proportions p described in part B is called the and the formula for this is o, =. D. According to the Mars company, packages of milk chocolate M&Ms contain 20% orange candies. Suppose we examine 100 random candies. If we took random samples of 100 M&Ms over and over again and calculated the proportion of orange candies p, what would the mean of the sampling distribution of these p values be? =. What is the standard error? o, E. Check that the conditions for the Central Limit Theorem for Sample Proportions are met. For 1) and 3), just confirm with a brief statement. For 2), do the calculations. These conditions are: 1) Random and Independent Samples np 10 2) Large Sample: -p) 210 3) Big Population: Population at least 10 times the sample size. Focus Since these are met, apply the Central Limit Theorem for Sample Proportions. State the distribution of p and draw its sketch, labeling the mean and 3 standard deviations on each side of the mean. Note: Just draw the sketch with the mean & Standard error calculated above in part D. I F. Use the result from part E to find the probability that a random sample of 100 M&Ms has more than 25 orange candies. That is, find P(p>0.25). Include a sketch with the area of interest shaded, write what you entered in to StatCrunch, and write your answer as part of a complete sentence.

Answer 1

A) sampling distribution

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B) u P

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Standard error

P1-P C) oB

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|D) 0.20

(02* 0.8)/100 0.04 O