Let\'s examine the mean of the numbers 1, 2, 3, 4, 5, 6,7, and 8 by drawing samp

Question

Let's examine the mean of the numbers 1, 2, 3, 4, 5, 6,7, and 8 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 an eight-sided die two times (or equivalently, roll two eight-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, and 8. The true mean () of the numbers 1, 2, 3, 4, 5, 6, 7, and 8 is ,and the true standard deviation (a) is The number of possible different samples (each of size n 2) is the number of possibilities on the first roll (8) times the 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 ( ) would equal sampling distribution of means (that is, the standard error or would be , and the standard deviation of your 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 less than or equal to 1.5, or P(M 1.5), is The probability that the mean of your two rolls is

Explanation / Answer

True mean = [1+2+3+4+5+6+7+8 ]/ 8 =4.5

True Standard Deviation = 2.449

Sampling mean = True mean = 4.5

Standard error = 0.866

Probability that mean of two rolls is equal to true mean = 8/64=0.125

Probability that mean is less than equal to 1.5 = (1+2)/64 = 3/64

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