Question

4. As the newly hired manager of a company that provides cell phone service, you want to determine the percentage of adults in your state who live in a household with cell phones and no land-line phones. How many adults must you survey? Assume that you want to be 90% confident that the sample percentage is within three percentage points of the true population percentage. Use STATCRUNCH to calculate the following Sample Size. a. Assume that nothing is known about the percentage of adults who live in a household with cell phones and no land-line phones. n = Concluding Statement: (Round UP) b. Assume that a recent survey suggests that about 8% of adults live in a household with cell phones and no land-line phones (based on data from the National Health Interview Survey). n = Concluding Statement: (Round UP)

Answer 1

Solution :

Given that,

$\hat p$ = 1 - $\hat p$ = 0.5

margin of error = E = 0.03

At 90% confidence level

$\alpha$ = 1 - 90%

$\alpha$ =1 - 0.90 =0.10

$\alpha$/2 = 0.05

Z$\alpha$/2 = 1.645

sample size = n = (Z_{$\alpha$ / 2} / E )² * $\hat p$ * (1 - $\hat p$ )

= (1.645 / 0.03)² * 0.5 * 0.5

= 751.67

sample size = n = 752

b)  $\hat p$ = 0.08

1 - $\hat p$ = 1 - 0.08 = 0.92

sample size = n = (Z_{$\alpha$ / 2} / E )² * $\hat p$ * (1 - $\hat p$ )

= (1.645 / 0.03)² * 0.08 * 0.92

= 221.29

sample size = n = 222