Forecasting. A REVIEW OF BASIC STATISTICAL CONCEPTS

Forecasting. A REVIEW OF BASIC STATISTICAL CONCEPTS

CHAPTER 2

A REVIEW OF BASIC STATISTICAL CONCEPTS

ANSWERS TO ODD-NUMBERED PROBLEMS AND CASES

1. Descriptive Statistics

Variable N Mean Median StDev SE Mean
Orders 28 21.32 17.00 13.37 2.53

Variable Min Max Q1 Q3

Orders 5.00 54.00 11.25 28.75

a. [pic] = 21.32
b. S = 13.37
c. S2 = 178.76
d. If the policy is successful, smaller orders will be eliminated and the mean will
increase.

e. If the change causes all customers to consolidate a number of small orders into
large orders, the standard deviation will probably decrease. Otherwise, it is very
difficult to tell how the standard deviation will be affected.

f. The best forecast over the long-term is the mean of 21.32.

3. a. Point estimate: [pic]

b. 1(( = .95 ( Z = 1.96, n = 30, [pic]
[pic]
(5.85%, 15.67%)

c. df = 30(1 = 29, t = 2.045
[pic]
(5.64%, 15.88%)

d. We see that the 95% confidence intervals in b and c are not much different because the multipliers 1.96 and 2.045 are nearly the same magnitude.
This explains why a sample of size n = 30 is often taken as the cutoff between
large and small samples.

5. H0: ( = 12.1 n = 100 ( = .05
H1: ( > 12.1 S = 1.7 [pic] = 13.5

Reject H0 if Z > 1.645

Z = [pic]= 8.235

Reject H0 since the computed Z (8.235) is greater than the critical Z (1.645). The mean has increased.

7. n = 60, [pic]
[pic] two-sided test, ( = .05, critical value: |Z|= 1.96
Test statistic: [pic]

Since |(2.67| = 2.67 > 1.96, reject [pic] at the 5% level. The mean satisfaction rating is...