STAT 2112 GWU Statistics Average Price Spent Problems

STAT2112.10
Quiz # 6 NAME:________________GWID:G_________________
Fall 2022 sba (TakeHome portion) – Due on Monday (Dec 4) at 7:30PM
Please answer all the questions using a simple calculator and
SHOW ALL YOUR WORK
Problem 1. When John started his freshman year at GWU, his parents decided to create a basket
of items that included his spending on major items so they can track his spending and compute
inflation rates for the basket. John is now a junior (finishing up his 6th semester at GWU). His
parents have the complete data until the end of 5th semester. To save you computation time, I
included only three items from the basket:
Item 1: Textbook
Item 2: Eating at High End Restaurants
Item 3: Electronic items/Cell phones/laptop/tablet
t Semester
1
S1
2
S2
3
S3
4
S4
5
S5
6
S6
Quantity of items
1
2
3
7
3
5
5
5
2
8
2
3
10
4
0
6
5
1
–
t Semester
1
S1
2
S2
3
S3
4
S4
5
S5
6
S6
Average Price of each item ($)
1
2
3 .
$70
$35
$200
$100 $50
$500
$60
$80
$400
$80
$40
$300
$120 $50
$900
–
Use the information provided above, answer (compute) all the questions (CPIs) below:
a) Laspeyres price index for Semester 4 (S4) – .25 point
b) Paasche Price Index for Semester 4 (S4) – .25 point
c) Fisher for Price Index for Semester 4 (S4) – 0.25 point
d) Lowe’s Price Index for Semester 4 (S4) – .25 point — For this, use S3 basket as the base
e) Establish a Run chart (Chapter 13) for total textbook price only (identify the center line
and upper/control limits using the data provided) — here, your answer can be based on
the total spending on the textbook per semester — All I want for you is to establish a
norm (center line and upper/lower control limits based on 6-sigma rule) – .5 point
Problem 2. Using the average price spent on Electronic items/Cell phones/laptop/tablet, provided
above, as our time series data,
a) Using the moving average of two period forecast the spending on this item for Semesters
6 and 8 (0.25 pt)
b) Using simple exponential smoothing method and w=0.40, forecast the spending for this
item in Semesters 6 and 8 (.25 pt)
c) Using double exponential smoothing method and w=0.40, υ=0.2, forecast the spending
for this item in Semesters 6 and 8 (.5 pts)
Problem 3. Using the average price spent on Electronic items/Cell phones/laptop/tablet, provided
above, compute Autocorrelation of lag 1 and lag 2. (0.5 for each)
Problem 4. Two forecasting methods have produced the following forecast for the past five
months.
Actual
Forecast 1
Forecast 2
.
10
11
9
8
10
7
10
8
11
6
6
7
9
8
10.
a) Compute all three popular measures of forecast accuracy for the Forecast 1.(0.5 pt)
b) Compute all three popular measures of forecast accuracy for the Forecast 2.(0.5 pt)
c) Based on the results for MAD (mean absolute deviation) statistics which forecast method
do you recommend? (0.5 pt)