Question

using a random sample of 3648 tv households, acme media statistics found that 37.3% watched the final episode of \it aint over yet.\
a. find the margin of error in this percent
b. write a statement about the percentage of tv households in the population who turned into the final episode of \it aint over yet.\
a. the margin of error is ± 1.66%.
(do not round until the final answer. then round to the nearest hundredth as needed.)
b. complete the following statement.
we can be 95% confident that between □% and □% of all households watched the final episode of \it aint over yet.\
(use ascending order. round to the nearest hundredth as needed.)

Explanation:

Step1: Calculate the lower and upper bounds

The sample proportion \(p = 37.3\%\) or \(p=0.373\), and the margin of error \(E = 1.66\%\) or \(E = 0.0166\)

The lower bound \(=p - E\)

$$=0.373-0.0166=0.3564 = 35.64\%$$

The upper bound \(=p + E\)

$$=0.373 + 0.0166=0.3896=38.96\%$$

Answer:

a. The margin of error is \(1.66\%\)
b. We can be \(95\%\) confident that between \(35.64\%\) and \(38.96\%\) of all households watched the final episode of "It Ain't Over Yet."