Central Theorom

Central Limit Theorem (Week 2)

QNT/561

January 5, 2011

Week 2 Assignment: Exercises 21, 22, and 34 (Ch. 8) of Statistical Techniques in Business & Economics:

#21 (a-c) a. The difference between the sample mean (bar X) and the population mean.

b. Yes.

c. The sample size is equal to the populations size

#22 (a-d) Reasons for sampling:

a. Time: Surveying and entire population can be time consuming. Sampling a small group can be quick and more efficient.

b. Cost: The cost to conduct a sampling will be more effective.

c. Accuracy: Small groups that are sampled can provide you with similar results in accuracy.

d. Destructive sampling -- for example, if you crash tested the entire population of cars for safety testing, you wouldn't have any left to drive -- so you only test a sample

#34 (a-e)

a. 5656.85

b. Normal distribution

c. z = (112000-110000)/5656.85

z = 0.353553

from a z table...

prob(z > 0.353553)

= 0.3618

excel:

=1-NORMDIST(112000,110000,5657,TRUE)

d. z = (100000-110000)/5656.85

z = -1.767768

from a table:

prob(z > -1.767768)

= 0.9615

in excel:

=1-NORMDIST(100000,110000,5657,TRUE)

e. Part D - Part C:

= 0.9615 - 0.3618

= 0.5997

excel:

=1-NORMDIST(100000,110000,5657,TRUE)-(1-NORMDIST(112000,110000,5657,TRUE))

Exercises 32, 34, and 46 (Ch. 9) of Statistical Techniques in Business & Economics

#32 mean - z*sd/sqrt(N) to mean + z*sd/sqrt(N)

z (from a table) is 1.96

N = 36

sd = 0.03

mean = 3.01  (continued next page) 

3.01 - 1.96*0.03/sqrt(36) to 3.01 + 1.96*0.03/sqrt(36)

3.0002 to 3.0198

#34 n = 50, m = 26, s = 6.2,

SE of the mean = s/sqrt n = 6.2/sqrt 50 = 0.8768, z = 1.96

Margin of error: E = Z * SE = 1.96 * 0.8768 = 1.7186

Lower Limit of the confidence interval = m - E = 24.2814 

Upper Limit of the confidence interval = m + E = 26 + 1.7186 = 27.7186

Therefore, the confidence interval...