Suppose that, in order to estimate the proportion of students who wear glasses, a sample of 100 students was collected and showed that 20 of the students in the sample wore glasses. A confidence interval for the population proportion of students who wear glasses is given by: .200 +/- 3.000(.040) or .080 to .320. (Note that the standard error is .040.) Which one of the following statements would the confidence interval tend to support?
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99.7 because the multiplier is 3.00
The confidence interval for the proportion of students who wear glasses is .080 to .320. This means that we are 95% confident that the true population proportion is within this range based on our sample.
In order to determine which statement the confidence interval tends to support, we need to consider which statements fall within the range of the confidence interval.
Statement 1: The proportion of students who wear glasses is 0.25.
Since 0.25 is not within the range of .080 to .320, the confidence interval does not support this statement.
Statement 2: Most students wear glasses.
The word "most" is vague, but if we interpret it as meaning more than 50% of students, then the range .080 to .320 does support this statement. This is because 50% (or 0.5) falls within the interval.
Statement 3: Few students wear glasses.
The word "few" is also vague, but if we interpret it as meaning less than 50% of students, then the range .080 to .320 does not support this statement. This is because 50% (or 0.5) is not within the interval.
Therefore, the confidence interval tends to support statement 2: Most students wear glasses.