Based on a recent poll of 1,015 U.S. households that have an Internet connection, the researchers claimed with 95% confidence that among all U.S. households that have an Internet connection, between 63% and 67% have a high-speed link.point estimationinterval estimationhypothesis testing
Question
Based on a recent poll of 1,015 U.S. households that have an Internet connection, the researchers claimed with 95% confidence that among all U.S. households that have an Internet connection, between 63% and 67% have a high-speed link.point estimationinterval estimationhypothesis testing
Solution
The researchers are using interval estimation in this case. This is because they are estimating a range (between 63% and 67%) within which the true population parameter lies with a certain level of confidence (95%).
Here's the step-by-step process:
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The researchers conducted a poll of 1,015 U.S. households that have an Internet connection. This is the sample.
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They calculated the proportion of this sample that have a high-speed link. This is the sample statistic.
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They then used this sample statistic to estimate the proportion of all U.S. households with an Internet connection that have a high-speed link. This is the population parameter.
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Instead of providing a single value (point estimate), they provided a range (interval estimate) within which they are 95% confident that the true population parameter lies.
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The range of 63% to 67% is the confidence interval. The researchers are 95% confident that the true proportion of all U.S. households with an Internet connection that have a high-speed link is within this interval.
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