Question

Rachel is conducting a study in her cognitive psychology lab about people's ability to remember rhythms. She played a short Rhythm to 425 randomly chosen people. One minute later, she asked him to repeat it by clapping. If 121 people were able to successfully reproduce the rhythm, estimate the proportion of the population (including the margin of error) that would be able to successfully reproduce the rhythm.

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Answer 1

a. 28.47% ± 4.37%

Explanation:

The sample proportion is ...

p = 121/425 ≈ 0.2847 = 28.47%

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The margin of error depends on the desired level of confidence. For a level of confidence of about 95%, the margin of error is about ...

±2 × √((p(1 -p)/(sample size)) = ±2×√(.2847·.7153/425) ≈ ±0.0438 = ±4.38%

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Comment on the last decimal place

The multiplier shown as 2 in the formula above corresponds to a confidence level of about 95.45%. The multiplier for 95% is 1.95996, and that gives a margin of error of ±4.29%. The multiplier that causes the margin of error value to round to 4.37% will be between 1.96 and 2, and will have a corresponding confidence level between 95% and 95.5%.

We don't know the confidence level or multiplier you are expected to use for this problem. The multiplier is almost certainly greater than 1, which corresponds to a confidence level of about 68%. Hence the appropriate answer choice will be somewhat larger than ±2.19%. A confidence level of 95% is pretty typical.