Question

URULLIY Worksheet 7: Sampling distribution of the Mean Using sampling distributions to answer questions about probability (25 points). The IQ distribution has a u=100 & a 0-15. IQ score distribution (same as IQ sampling distribution for n=1) 1. Label the distribution of IQ scores in raw score (4) units (1 point) 2. Mark the location of an IQ score=105 on the score distribution (-5 point) Z = X-M = 105 - 100 15 ² ss 100 115 hoi = 5 = 6.33 3. Calculate standard error of the mean (om) for each of the sampling distributions below (2 points). Om for n=9 5 Om for n-36 6-15 -15 -5 15 -2.5 Om 39 IQ sampling distribution: = 9 IQ sampling distribution: n=36 -2 -1 0 +1 +2 -2 -1 0 +1 +2 4. Label each of the sampling distributions in raw sample mean (M) units (2 points). 5. Mark the location of a sample mean-105 on each of the sampling distributions (I point). 6. Answer the questions/find the requested values for all 3 distributions in the table at the top of the next page (13.5 points):

Answer 1

1:

The interval corresponding to one standard deviation of mean is

$\mu\pm \sigma=100\pm 15=(85,115)$

The interval corresponding to 2 standard deviations of mean is

$\mu\pm 2\sigma=100\pm 30=(70,130)$

The interval corresponding to 3 standard deviations of mean is

$\mu\pm 3\sigma=100\pm 45=(55,145)$

Following is the graph:

5 70 85 100 105 130 145

2:

Following is the distribution with marked location:

55 70 85 X=105 100 105 130 145

3:

For n=9:

The standard error of mean is

$\sigma_{M}=\frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{9}}=5$

For n=36:

The standard error of mean is

$\sigma_{M}=\frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{36}}=2.5$

4:

For n=9:

85 90 95 100 105 110 115

For n=36:

92.5 95 97.5 100 102.5 105 107.5

5:

For n=9:

xbar=105 85 90 95 100 105 110 115

For n=36:

92.5 95 97.5 100 102.5 xbar=105 105 107.5