Let's examine the mean of the numbers 1, 2, 3, 4, 5, 6, Ir, and E by drawing samples from these values, calculating the mean of each sample,...

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Let's examine the mean of the numbers 1, 2, 3, 4, 5, 6, Ir", and E by drawing samples from these values, calculatingthe mean of each sample, and then considering the sampling distribution of the mean. To do this, suppose youperform an experiment in which you roll an eight-sided die two times {or equivalently, roll two eight-sided dioe onetime} and calculate the mean of your sample. Remember that your population is the numbers 1, 2, 3, 4-, 5, 6, Ir", andE. The true mean {u} of the numbers 1, 2, 3, 4, 5, 6, 7", and E is , and the true standard deviation {0) is The number of possible different samples {each of size n = 2) is the number of possibilities on the first roll {3) timesthe number of possibilities on the second roll {also 8}, or 8(8) = 64-. If you collected all of these possible samples.the mean of your sampling distribution of means {pm} would equal , and the standard deviation of yoursampling distribution of means {that is, the standard error or on) would be The following chart shows the sampling distribution of the mean {M} for your experiment. Suppose you do thisexperiment once {that is, you roll the die two times). Use the chart to determine the probability that the mean ofyour two rolls is equal to the true mean, or PM = p}, is . The probability that the mean of your two rolls isless than or equal to 1.5, or P{M 5 1.5}, is