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Question bank: Statistics: Sample Surveys

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Question 1:

Very Hard

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.
Statistics: Sample Surveys
Question 2:

Hard

Considering a population of 1000 students in a school, a sample survey was conducted with 100 randomly chosen students. The results indicated that 70% of the students enjoy practicing physical activities after class. Based on this data, what is the estimate of how many students in this school enjoy practicing physical activities after class?
Statistics: Sample Surveys
Question 3:

Medium

João is a student who is conducting a research on soda consumption in his school. He interviewed 50 students of different ages to analyze the results. Which of the following measures are measures of central tendency that can be used to analyze the data collected by João?
Statistics: Sample Surveys
Question 4:

Medium

The 11th-grade class of XYZ school is planning a fundraising party and wants to know which type of food is the most popular among students. To find out, they decide to conduct a sample survey with students from the entire school, which has a total of 1,500 students. Based on this context, answer the following questions:
Statistics: Sample Surveys
Question 5:

Medium

Statistics: Sample Surveys
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