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CENGAGE MINDTAP Problem Set: Chapter 07 Probability and Samples: The Distribution of Sample Means 3. Generating the sampling distribution of M Let's examine the mean of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 by drawing samples from these values, calculating the mean of each sample, and then considering the sampling distribution of the mean. To do this, suppose you perform an experiment in which you roll a ten-sided die two times (or equivalently, roll two ten-sided dice one time) and calculate the mean of your sample. Remember that your population is the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. The true mean (u) of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 is , and the true standard deviation (o) is The number of possible different samples (each of size n = 2) is the number of possibilities on the first roll (10) times the number of possibilities on the second roll (also 10), or 10(10) = 100. If you collected all of these possible samples, the mean of your sampling distribution of means (UM) would equal , and the standard deviation of your sampling distribution of means (that is, the standard error or OM) would be The following chart shows the sampling distribution of the mean (M) for your experiment. Suppose you do this experiment once (that is, you roll the die two times). Use the chart to determine the probability that the mean of your two rolls is equal to the true mean, or P(M = (), is The probability that the mean of your two rolls is greater than 1.5, or P(M > 1.5), is 12 10 8 - Frequency A 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 M