Suppose an x distribution has mean = 3. Consider two corresponding x distributio

Question

Suppose an x distribution has mean = 3. Consider two corresponding x distributions, the first based on samples of size n = 49 and the second based on samples of size n = 81. (a) What is the value of the mean of each of the two x distributions? For n = 49, x = For n = 81, x = (b) For which x distribution is P( x > 3.75) smaller? Explain your answer. The distribution with n = 81 because the standard deviation will be larger. The distribution with n = 49 because the standard deviation will be smaller. The distribution with n = 81 because the standard deviation will be smaller. The distribution with n = 49 because the standard deviation will be larger. (c) For which x distribution is P(2.25 < x < 3.75) greater? Explain your answer. The distribution with n = 49 because the standard deviation will be smaller. The distribution with n = 81 because the standard deviation will be smaller. The distribution with n = 81 because the standard deviation will be larger. The distribution with n = 49 because the standard deviation will be larger.

Explanation / Answer

a)

(a) What is the value of the mean of each of the two x distributions?

For n = 49, x = n*u = 49*3 = 147 [ANSWER]

For n = 81, x = n*u = 81*3 = 243 [ANSWER]

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b)

This interval does not include the mean (u = 3), so it will have smaller probability for larger n, because the variation decreases.

ANSWER: The distribution with n = 81 because the standard deviation will be smaller. [ANSWER]

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c)

As this includes the mean (u = 3), then it is more probablt when n is larger due to lesser variation around the mean,

ANSWER: The distribution with n = 81 because the standard deviation will be smaller.

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