Understanding Variance, Standard Deviation, and Sampling Distributions in R



 A.


B.   Sample = {14, 10}


C.               

Squared deviations:




D. Deviations and squared deviations:

X

 

 

 

 

 

x - μ

 

 

 

 

 

 

 

 

 

(x - μ)²

8

 

 

 

 

 

-3.8

 

 

 

 

 

 

 

 

 

14.44

14

 

 

 

 

 

2.2

 

 

 

 

 

 

 

 

 

4.84

16

 

 

 

 

 

4.2

 

 

 

 

 

 

 

 

 

17.64

10

 

 

 

 

 

-1.8

 

 

 

 

 

 

 

 

 

3.24

11

 

 

 

 

 

-0.8

 

 

 

 

 

 

 

 

 

0.64

Total

 

 

 

 

 

 

 

 

 

 

 

 

 

 

40.8

Sample #

Values

Mean

Sample 1:

14, 10

(14 + 10)/2 = 12

Sample 2:

8, 16

(8 + 16)/2 = 12

Sample 3:

11, 14

(11 + 14)/2 = 12.5

Standard Error:

  



1. Does the sample proportion p have approximately a normal distribution?

- Yes, the sample proportion does have an approximately normal distribution.

  np = 0.95 × 100 = 95

  nq = 0.05 × 100 = 5

2. What is the smallest value of n for which the sampling distribution of p is approximately normal?  

-  Yes, the smallest sample size  for which the sampling distribution of the sample proportion is approximately normal is 100




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