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 them to repeat it by clapping. If 121

people were able to successfully reproduce the rhythm, estimate the proportion of the population (including margin

of error) that would be able to successfully reproduce the rhythm.

Answer 1

Rachel can conclude that 28% were able to successfully reproduce the rhythm plus or minus 5.6%

Explanation:

To find the sample proportion that is able to successfully reproduce the rhythm = 121/425 = 0.2847 = p

Using this formula, we can calculate the margin of error

Margin of error = z*√{[p (1-p)] / n}

Where we assume a 95% level of confidence so that z* = 1.96. since one is not given, p = 0.28457 and n = 245.

Margin of error = 1.96 x √(0.28457 (1-0.28457)] / 245}

Margin of error = 1.96 x √[(0.28457 (0.7154)] / 245

= 1.96 x √(0.20/245)

= 1.96 x √0.000816

= 1.96 x 0.03

= 0.056.

Thus, Rachel can conclude that 28% were able to successfully reproduce the rhythm plus or minus 5.6%