(Originais Teachy 2023) - Question Very Hard of Mathematics

A cosmetics industry wants to evaluate consumer satisfaction regarding a new hair product. They conduct a satisfaction survey with a representative sample of consumers. The sample is stratified according to age groups, with 20% of the respondents belonging to the 18-25 age group, 30% to the 26-35 age group, 25% to the 36-45 age group, and 25% to the 46-60 age group. When analyzing the survey results, the company realizes that the average satisfaction of consumers is 4.5 on a scale of 1 to 5, where 1 is 'very dissatisfied' and 5 is 'very satisfied'. However, they suspect that satisfaction may be influenced by the age group distribution in the sample. To investigate this hypothesis, they conduct a statistical simulation where they keep the consumers' responses constant but change the age group distribution so that all strata have the same weight in the sample. After this simulation, the average satisfaction of consumers changes to 4.3. Considering the concept of sampling and stratified analysis, discuss how the change in age group distribution can affect the average satisfaction of consumers and evaluate the reliability of the initial survey results.