Calculating Sample Size for Proportion Estimation

[toothpaste666]

Homework Statement

1. A national safety council wishes to estimate the proportion of automobile accidents that involve pedestrians. How large a sample of accident records must be examined to be 99% certain that the estimate does not differ from the true proportion by more than 0.03? Answer the question if
   
   (a) the council believes that the true proportion is 0.2.
   
   (b) no information about the true proportion is given.
   

The Attempt at a Solution

α = .01 , α/2 = .005, z.005 = 2.575
a) n = p(1-p) [zα/2/E]^2
= (.2)(.8)[2.575/.03]^2 = 1179

b) n = .25[zα/2/E]^2 = (.25)[2.575/.03]^2 = 1842

is this correct?

 

[Ray Vickson]

Homework Statement

1. A national safety council wishes to estimate the proportion of automobile accidents that involve pedestrians. How large a sample of accident records must be examined to be 99% certain that the estimate does not differ from the true proportion by more than 0.03? Answer the question if
   
   (a) the council believes that the true proportion is 0.2.
   
   (b) no information about the true proportion is given.

The Attempt at a Solution

α = .01 , α/2 = .005, z.005 = 2.575
a) n = p(1-p) [zα/2/E]^2
= (.2)(.8)[2.575/.03]^2 = 1179

b) n = .25[zα/2/E]^2 = (.25)[2.575/.03]^2 = 1842

is this correct?

(1) Have you used the correct formulas?
(2) Have you used the formulas correctly?
(3) Have you made no arithmetical errors?

If your answer to (1)--(3) is YES, then your answer will be correct.

You need to start having confidence in your own work. Frankly, your endless series of similar questions is starting to get old.

 

[toothpaste666]

I apologize. This is the first stats class I have taken, so I wanted to make sure I understand the differences between all the different cases and that I am using the correct statistic for the correct problems. It is because I am reviewing for a final. I won't post any more hypothesis testing questions.

 

[mfb]

You can test the reverse direction. Given a sample of n=1179 with p=0.2, how likely is a deviation of 0.03 or more?