32. In a survey of 300 people who were randomly sampled from a well-defined population, 60 said that they read a newspaper daily. If 1,000 people had been randomly sampled from the same population and asked the same question, how many would be expected to say they read a newspaper daily?
Answer: A
180 people would be expected to say they read a newspaper daily.
In the survey, 60 out of 300 people reported reading a newspaper daily, which gives a proportion of 20%. If 1,000 people were sampled, we would expect 20% of that number to read a newspaper daily, resulting in 200 individuals.
A) 180
This option is incorrect. Although it is a reasonable estimate, the calculation based on the proportion derived from the initial survey indicates that 200 people would be expected to read a newspaper daily.
B) 200
This option is correct. The calculation is based on the proportion of individuals who read a newspaper daily in the initial survey (60 out of 300, which is 20%). When applied to a sample size of 1,000, this proportion would yield 200 expected respondents.
C) 360
This option is incorrect. This figure represents a higher proportion than the calculated 20% of the population, which is not supported by the original survey data.
D) 600
This option is also incorrect. A figure of 600 implies an unrealistic proportion of 60% of the population reading a newspaper daily, which is significantly higher than the observed 20%.
E) 760
This option is incorrect as well. It suggests an even greater percentage of the population reading newspapers daily, which is not supported by the survey's findings indicating only 20% of respondents.
Conclusion
The correct expected number of individuals reading a newspaper daily, based on the proportion from the survey, is 200. All other options fail as they either overestimate or underestimate the actual proportion of newspaper readers indicated in the survey data. This demonstrates the importance of applying accurate proportional reasoning in statistical estimations.