Question

A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think the drinking age should be lowered to 18. He asks, 'Do you think the drinking age should be reduced to 18 in light of the fact that 18 year olds are eligible for military service? He asks listeners to phone in and vote "yes" if they agree the drinking age should be lowered and "no" if not. Of the 100 people who phoned in, 70 answered "yes." The margin of error for a 90% confidence interval is
a. 0.045.
b. 0.074.
c. 0.089.
d. 0.690.

Answer 1

Answer:

$ME = 1.64\sqrt{\frac{0.7 (1-0.7)}{100}}= 0.074$

And the best answer would be:

b. 0.074.

Step-by-step explanation:

For this case we have the following info given:

$X= 70$ represent the number of people who answer yes for the question

$n= 100$ the sample size selected

$\hat p =\frac{X}{n}=\frac{70}{100}= 0.7$ the proportion estimated of people who answer yes

The margin of error is given by:

$ME = z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

The confidence level is 90% and the significance would be $\alpha=0.1$ and the critical value would be:

$z_{\alpha/2}= 1.64$

And replacing we got:

$ME = 1.64\sqrt{\frac{0.7 (1-0.7)}{100}}= 0.074$

And the best answer would be:

b. 0.074.