Suppose the probability is p = 0.36 that a person who purchases an instant lottery ticket wins money, and this probability holds for every ticket purchased. Consider different random samples of n = 36 purchased tickets. Let p̂ = sample proportion of winning tickets in a sample of 36 tickets. (a) Give the numerical value of the mean of the sampling distribution of p̂. (Round your answer to two decimal places.) Mean = .36 (b) Calculate the standard deviation, s.d. of the sampling distribution of p̂. (Round your answer to two decimal places.) s.d.(p̂) = 0.08 (c) Use the Empirical Rule to find values that fill in the blanks in the following sentence. (Round your answers to two decimal places.) In about 68% of all randomly selected samples of n = 36 instant lottery tickets, the proportion of tickets that will be money winners will be between and . (d) Use the Empirical Rule to find values that fill in the blanks in the following sentence. (Round your answers to two decimal places.) In about 95% of all randomly selected samples of n = 36 instant lottery tickets, the proportion of tickets that will be money winners will be between and .

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.