As discussed in exercise 6.10, the general social survey reported a sample where about 61% of us residents thought marijuana should be made legal. if we wanted to limit the margin of error of a 95% confidence interval to 2%, about how many americans would we need to survey?

2285

Step-by-step explanation:

Formula to find the sample size is given by :-

, where p = prior estimate of population proportion.

E= Margin of error.

= z-value for confidence interval of c.

Given : Confidence interval : 95%

From the z-value table , the z-value for 95% confidence interval =

The General Social Survey reported a sample where about 61% of US residents thought marijuana should be made legal.

i.e. the prior estimate of population proportion of US residents thought marijuana should be made legal : p=0.61  

 [∵ sample proportion is the best estimate for population proportion.]

Margin of error : E= 2%=0.02

Now, the required minimum sample size would be :-

Simplify ,

Thus , we need to survey 2285 Americans .

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)