Assume that the data below represent a population of N= 24 values.Complete parts

Question

Assume that the data below represent a population of N= 24 values.Complete parts a,b,and c.

22 25 22 13 26 23 10 11 14 31 23 13 31 14 14 11 23 26
8 13 15 15 15 28

a. If a random sample of n = 10 itemsincludes the values below,compute the sampling error for the sample mean. 15 26 23 14 11 22 13 28 13 14

The sampling error for the sample mean is __ (Round to two decimalplaces as needed.)

b. For a sample of size n=6,compute the range for the possible sampling error. (Hint: Find the sampling error for the 6 smallest sample values and the 6 largest sample 'alues.)

The possible sampling error ranges from __to __ (Round to two decimal places as needed.Use ascending order.)

c. For a sample of sze n= 12,compute the range for the possible sampling error. How does sample size affect the potentialfor extreme sampling error?

The possible sampling error ranges from __ to __ (Round to two decimal places as needed.Use ascending order.)

How does sample size affect the potentialfor extreme sampling error?

A. As the sample size increases,the sampling error becomes more positive.

B. As the sample size increases,the sampling error becomes more negative.

C. As the sample size increases,the range of sampling error decreases .

D. Sample size has no effect on the sampling error.

E. As the sample size increases,the range of sampling error increases.

Explanation / Answer

a) sample mean = ( 15 + 26 + 23 + 14 + 11 + 22 + 13 +28 + 13 + 14) /10

= 17.9

Population mean = (22 + 25 + 22 + 13+ 26+ 23 +10 +11 +14 +31 + 23 +13 +31 + 14+14 +11 + 23 + 26 +8+ 13 +15 +15 +15 +28)/24

= 18.58

sampling error = ( sample mean - population mean)

= 17.9 - 18.58 = -0.68

b) Smallest values = (8 + 10 + 11 + 11 + 13 + 13) / 6 = 11

largest values = (25 + 26 + 26+ 28 + 31 +31)/6 = 27.83

Smallest sample mean. The sampling error is = 11 - 18.58 = -7.58

Largest  sample mean. The sampling error is = 27.83 - 18.58 = 9.25

Sampling error ranges from -7.58 to 9.25

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