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StatisticsQ&A LibrarySuppose an x distribution has mean μ = 2. 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, μx = For n = 81, μx = (b) For which x distribution is P(x > 2.5) smaller? 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 = 49 because the standard deviation will be larger.The distribution with n = 81 because the standard deviation will be larger.(c) For which x distribution is P(1.5 < x < 2.5) greater? Explain your answer.The distribution with n = 49 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 larger.The distribution with n = 81 because the standard deviation will be smaller.Question

Asked Feb 1, 2020

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Suppose an *x* distribution has mean μ = 2. 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

(b) For which*P*(

(c) For which*P*(1.5 <

x

distributions?
For n = 49, μ
x
= |

For n = 81, μ
x
= |

(b) For which

x

distribution is x

> 2.5) smaller? 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* = 49 because the standard deviation will be larger.The distribution with *n* = 81 because the standard deviation will be larger.

(c) For which

x

distribution is x

< 2.5) greater? Explain your answer.
The distribution with *n* = 49 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 larger.The distribution with *n* = 81 because the standard deviation will be smaller.

Step 1

Given

a)

x distribution has mean µ = 2

The mean of the sampling distribution is nothing but the population mean. So

for sample size n = 49 the mean µ = 2

for sample size n = 81 the mean µ = 2

Step 2

b)

For x distribution P( x > 2.5)

The standard deviation is inversly proportional to sample size. As the sample size increases the standard deviatio...

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