Suppose you want to estimate the proportion of traditional college students on your campus who own their own car. from research on other college campuses, you believe the proportion will be near 3030%. what sample size is needed if you wish to be % confident that your estimate is within 0.020.02 of the true proportion?

3484

Step-by-step explanation:

The following formula is used to compute the minimum sample size required to estimate the population proportion  within the required margin of error:

n≥ p×(1-p) × where

we have p=0.30 (30%) z=2.58 ME= 0.02 then we get

n≥ 0.3×(1-0.3) × = 3483.32

therefore we need at least 3484 students under these conditions.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}