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.
[tex]\frac{121}{425}\times100\%=28.47\%[/tex]Our sample proportion p = 28.47%.
Then, for the margin of error, the formula is:
[tex]MOE=z\sqrt{\frac{p(1-p)}{n}}[/tex]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.
[tex]MOE=1.645\sqrt{\frac{.2847(1-.2847)}{425}}[/tex]Then, solve.
[tex]MOE=1.645\sqrt{\frac{0.203648}{425}}[/tex][tex]MOE=1.645(0.02189)[/tex][tex]MOE=0.036[/tex]Let's multiply the MOE by 100%.
[tex]0.036\times100\%=3.6\%[/tex]Therefore, about 28.47% ± 3.6% or between 24.87% to 32.07% of the population would be able to successfully reproduce the rhythm.
