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A 鈥渞andom survey鈥� was conducted of 3,274 people of the 鈥渕icroprocessor generation鈥� (people born since 1971, the year the microprocessor was invented). It was reported that 48% of those individuals surveyed stated that if they had $2,000 to spend, they would use it for computer equipment. Also, 66% of those surveyed considered themselves relatively savvy computer users. a. Do you consider the sample size large enough for a study of this type? Why or why not? b. Based on your 鈥済ut feeling,鈥� do you believe the percents accurately reflect the U.S. population for those individuals born since 1971? If not, do you think the percents of the population are actually higher or lower than the sample statistics? Why? Additional information: The survey, reported by Intel Corporation, was filled out by individuals who visited the Los Angeles Convention Center to see the Smithsonian Institute's road show called 鈥淎merica鈥檚 Smithsonian.鈥� c. With this additional information, do you feel that all demographic and ethnic groups were equally represented at the event? Why or why not? d. With the additional information, comment on how accurately you think the sample statistics reflect the population parameters.

Step by step solution

01

Assessing Sample Size

To determine if the sample size of 3,274 is large enough, we consider common statistical standards. In survey research, a sample size of 1,000-1,500 is generally deemed sufficient for a high degree of precision in estimates of population parameters for large populations. Therefore, a sample size of 3,274 is more than adequate for general survey purposes and should yield reliable estimates, assuming the sample is well chosen.

02

Analyzing Representativeness of Statistics

To evaluate whether the survey鈥檚 reported percentages (48% and 66%) reflect the broader U.S. population, consider the nature of the sample. This was a convenience sample of attendees at a specific event, which introduces biases, as attendees are not necessarily representative of the entire population. Therefore, percentages might not fully represent all individuals born since 1971. A random, stratified sample from varied geographic and demographic regions would better capture the true population parameters.

03

Considering Demographic Representation

Given that the survey was administered at a specific event, 'America's Smithsonian' at the Los Angeles Convention Center, it's likely that attendees did not proportionally represent all demographic and ethnic groups. Event-goers may predominantly belong to certain demographics due to location, interest, and availability, leading to potential biases in representing the general population.

04

Evaluating Accuracy of Sample Statistics

With the additional information that the survey was taken at a specific event, it mitigates the reliability of the sample statistics to reflect true population parameters. The setting could have skewed the sample towards individuals with a keen interest in technology and computers, potentially resulting in an overestimation of both those who would spend money on computer equipment and those considering themselves savvy computer users.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Sample Size in Survey Methodology

When conducting a survey, the sample size is crucial in determining the precision of the results. A larger sample size typically means more reliable data, as it better captures the diversity and variations within a population.
In the provided exercise, a survey was conducted with a sample size of 3,274 people. This is considered a robust number because it surpasses the common threshold for sufficient precision in representing large populations, often set between 1,000 and 1,500 respondents.
Thus, a sample of 3,274 provides ample data to yield statistically reliable estimates of the population's parameters, assuming that the sampling method itself is unbiased and representative.

Ensuring Representativeness of a Sample

Representativeness in a survey means that the sample accurately reflects the demographics and diversity of the entire population. This is crucial for drawing conclusions that can be generalized beyond just the participants.
The exercise highlights potential issues with the sample's representativeness, as it was a convenience sample from a specific event. Attendees at a convention center might not represent all individuals born since 1971, introducing selection bias.
To improve representativeness, it would have been beneficial to use a random sampling method covering a broader geographic and demographic scope, thus including individuals from varied backgrounds.

Demographic Representation in Data Collection

Demographic representation ensures that all segments of the population are proportionally included in a survey. This is important to avoid skewing results toward a specific subset of the population.
The survey in question was conducted at "America鈥檚 Smithsonian" event, which may not have attracted a demographically balanced audience.
This could mean that certain ethnic or socio-economic groups were underrepresented, influencing the statistics gathered about attitudes toward computer equipment and user savviness.
It underlines the importance of broad accessibility and inclusivity in survey design to accurately mirror the population.

Interpreting Population Parameters

Population parameters are statistics that summarize and describe aspects of the entire population, like the average or proportion.
In any survey, the goal is to use the sample data to estimate these parameters accurately. However, when the survey setting introduces biases, as conducted at a specialized event, it may not accurately reflect the population at large.
The original survey results might have overestimated both the interest in computer equipment and the level of computer savviness due to a potentially tech-savvy demographic of attendees.
For accurate population parameter estimations, a diverse and unbiased sampling method across different segments of the population is crucial.