Respuesta :
Answer:
a. 1.52%
b. There is 95% probability that the true population percentage lies between 53.8$ and 56.62%
Step-by-step explanation:
The number of participants in the sample, n = 4,100
The percentage that watched the particular popular situation episode, p = 55.1%
a. The margin of error is given by the following formula;
[tex]Margin \ of \ Error = Z_{\alpha /2} \times \sqrt{\dfrac{p \times (1 - p)}{n} }[/tex]
Where;
Z = The z-score at 95% = 1.96
p = The proportion of the sample that responded positively = 55.1% = 0.551
n = 4,100
From the above data, we get;
[tex]Margin \ of \ Error = 1.96 \times \sqrt{\dfrac{0.551 \times (1 - 0.551)}{4,100} } \approx 0.0152252[/tex]
The margin of Error ≈ 1.52%
b. The confidence interval is give as follows;
[tex]p \pm Z_{\alpha /2} \times \sqrt{\dfrac{p \times (1 - p)}{n} }[/tex]
Therefore, we get the 95% confidence interval as follows'
55.1 - 1.52 ≤ μ ≤ 55.1 + 1.52
53.8% ≤ μ ≤ 56.62%
The answer as formatted in an online source is presented as follows;
There is 95% probability that the true population percentage lies between 53.8$ and 56.62%.
