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. Use a 95% confidence interval.

Answer 1

Given:

Sample Size (n) = 425

No. of Success = 121

Find: estimate the proportion of the population

Solution:

Let's calculate first the success proportion in the sample by dividing no. of success over the total number of people then multiply it by 100.

`(121)/(425)*100\%=28.47\%`

Our sample proportion p = 28.47%.

Then, for the margin of error, the formula is:

`MOE=z\sqrt{(p(1-p))/(n)}`

where z = critical value, p = sample proportion, and n = sample size.

For our z-value, since we are using a 95% confidence interval, the value of z = 1.645.

`MOE=1.645\sqrt{(.2847(1-.2847))/(425)}`

Then, solve.

`MOE=1.645\sqrt{(0.203648)/(425)}`
`MOE=1.645(0.02189)`
`MOE=0.036`

Let's multiply the MOE by 100%.

`0.036*100\%=3.6\%`

Therefore, about 28.47% ± 3.6% or between 24.87% to 32.07% of the population would be able to successfully reproduce the rhythm.