Calculating Sample Size for Proportion Estimation

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In summary: With p=0.25?In summary, to estimate the proportion of automobile accidents involving pedestrians, a national safety council must examine a sample of at least 1179 accident records with a confidence level of 99% and an estimated true proportion of 0.2. If no information about the true proportion is given, a larger sample of 1842 is needed to achieve the same confidence level. This assumes that the correct formulas have been used accurately and without arithmetical errors.
  • #1
toothpaste666
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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?
 
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  • #2
toothpaste666 said:

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.
 
  • #3
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.
 
  • #4
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?
 

1. What is the definition of "estimating a proportion"?

Estimating a proportion is a statistical process used to determine the likelihood or probability of an event occurring within a larger population. It involves collecting a sample from the population and using that information to estimate the proportion of the population that exhibits a certain characteristic or behavior.

2. How is "estimating a proportion" different from "calculating a proportion"?

Estimating a proportion involves using a sample to make an educated guess about the proportion in the entire population, while calculating a proportion involves using the exact values from the entire population to determine the proportion.

3. What are the steps involved in "estimating a proportion"?

The steps involved in estimating a proportion include: (1) selecting a representative sample from the population, (2) collecting data on the characteristic of interest in the sample, (3) calculating the sample proportion, (4) determining the margin of error, and (5) using the sample proportion and margin of error to estimate the population proportion.

4. Why is "estimating a proportion" important in research?

Estimating a proportion is important in research because it allows researchers to make inferences about a population based on a smaller sample. This can save time and resources, as well as provide valuable insights into the characteristics and behaviors of a larger group.

5. What are some potential limitations of "estimating a proportion"?

Some potential limitations of estimating a proportion include: (1) sampling bias, where the sample is not representative of the population, (2) small sample size, which can lead to inaccurate estimates, and (3) reliance on assumptions, such as the sample being randomly selected, which may not always hold true in real-world situations.

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