I don't think they are "sure", but the weights are based on the American Consumer Expenditure Survey which has a big sampling size, carefully chose sampling frame, professionally executed sample gathering, and experts crafting questions and collating the data.

How is the CPI market basket determined?

The CPI market basket is developed from detailed expenditure information provided by families and individuals on what they actually bought. For the current CPI, this information was collected from the Consumer Expenditure Surveys for 2011 and 2012. In each of those years, about 7,000 families from around the country provided information each quarter on their spending habits in the interview survey. To collect information on frequently purchased items, such as food and personal care products, another 7,000 families in each of these years kept diaries listing everything they bought during a 2-week period.

Over the 2 year period, then, expenditure information came from approximately 28,000 weekly diaries and 60,000 quarterly interviews used to determine the importance, or weight, of the more than 200 item categories in the CPI index structure.

Consumer Price Index Frequently Asked Questions (FAQs)

Consumer expenditure data supplied by the CE Survey are a critical component of the CPI, as they are used to estimate weights for the CPI’s consumer goods and services classification structure used in the calculation of the CPI. In the construction of the CPI, four distinct functional uses of CE Survey data are made: (1) to estimate biennial expenditure weights, (2) to estimate monthly expenditure weights, (3) to calculate the probability that an item’s price will be included in the CPI calculations, and (4) to allocate expenditure estimates between more-broadly defined expenditure categories from other survey sources.

Research highlights of the Consumer Expenditure Survey redesign

Page 6 of BLS Handbook of Methods, April 1997, Chapter 16: Consumer Expenditures and Income has a nice, detailed description of how "The estimation of population quantities of interest, such as the average expenditure per consumer unit on a particular item category, is achieved through the use of weights." Be sure to check that out too.

I don't think they are "sure", but the weights are based on the American Consumer Expenditure Survey which has a big sample size, a carefully chosen sampling frame, professionally executed sample gathering, and a large team of experts crafting questions and collating the data.

How is the CPI market basket determined?

The CPI market basket is developed from detailed expenditure information provided by families and individuals on what they actually bought. For the current CPI, this information was collected from the Consumer Expenditure Surveys for 2011 and 2012. In each of those years, about 7,000 families from around the country provided information each quarter on their spending habits in the interview survey. To collect information on frequently purchased items, such as food and personal care products, another 7,000 families in each of these years kept diaries listing everything they bought during a 2-week period.

Over the 2 year period, then, expenditure information came from approximately 28,000 weekly diaries and 60,000 quarterly interviews used to determine the importance, or weight, of the more than 200 item categories in the CPI index structure.

Consumer Price Index Frequently Asked Questions (FAQs)

Consumer expenditure data supplied by the CE Survey are a critical component of the CPI, as they are used to estimate weights for the CPI’s consumer goods and services classification structure used in the calculation of the CPI. In the construction of the CPI, four distinct functional uses of CE Survey data are made: (1) to estimate biennial expenditure weights, (2) to estimate monthly expenditure weights, (3) to calculate the probability that an item’s price will be included in the CPI calculations, and (4) to allocate expenditure estimates between more-broadly defined expenditure categories from other survey sources.

Research highlights of the Consumer Expenditure Survey redesign

Page 6 of BLS Handbook of Methods, April 1997, Chapter 16: Consumer Expenditures and Income has a nice, detailed description of how "The estimation of population quantities of interest, such as the average expenditure per consumer unit on a particular item category, is achieved through the use of weights." Be sure to check that out too.