statistics exam

Index Numbers Statistics (exercises)

Aleksandra Pawłowska

Jun 16, 2020

Task 1

The median sales prices for new single-family houses for the years 2004–2007 are as follows (Census Bureau website, March 19, 2009).

1 Use 2004 as the base year and develop a price index for new single-family homes over this four-year period.

2 Use 2005 as the base year and develop a price index for new single-family homes over this four-year period.

Aleksandra Pawłowska Index Numbers

Task 1 – solution

1 Use 2004 as the base year and develop a price index for new single-family homes over this four-year period. 100, 109, 111.5, 112.2

2 Use 2005 as the base year and develop a price index for new single-family homes over this four-year period. 91.7, 100, 102.3, 102.9

Aleksandra Pawłowska Index Numbers

Task 2

Nickerson Manufacturing Company has the following data on quan- tities shipped and unit costs for each of its four products:

1 Compute the price relative for each product. 2 Compute a weighted aggregate price index that reflects the

shipping cost change over the four-year period.

Aleksandra Pawłowska Index Numbers

Task 2 – solution

1 Compute the price relative for each product. 151.4, 196.9, 142.6, 177.5

2 Compute a weighted aggregate price index that reflects the shipping cost change over the four-year period. 170

Aleksandra Pawłowska Index Numbers

Task 3

Use the price data in task 2 to compute a Paasche index for the shipping cost if 2009 quantities are 4000, 3000, 7500, and 3000 for each of the four products.

Aleksandra Pawłowska Index Numbers

Task 3 – solution

Use the price data in task 2 to compute a Paasche index for the shipping cost if 2009 quantities are 4000, 3000, 7500, and 3000 for each of the four products. 163.7

Aleksandra Pawłowska Index Numbers

Task 4

Consider the following price relatives and quantity information for grain production in Iowa (Census Bureau website, March 19, 2009).

What is the 2007 weighted aggregate price index for the Iowa grains?

Aleksandra Pawłowska Index Numbers

Task 4 – solution

What is the 2007 weighted aggregate price index for the Iowa grains? 182.8

Aleksandra Pawłowska Index Numbers