# Solve Point Estimation Problems: 95% Confidence, 3% Error

• mikemike123
In summary: Note that your p is not the 16% you have been using, it is the "p" from the statement "estimate the proportion of all male electrical engineers who smoke regularly to within 3% of its true value".)In summary, the conversation revolved around solving two problems related to estimating proportions and sample sizes. The first problem involved finding the number of male electrical engineers needed to estimate the proportion of smokers with 95% confidence and a 3% margin of error. The second problem dealt with determining the maximum error and sample size needed in a study on meteorites entering the Earth's atmosphere. The formula used for estimating sample size was discussed, with a reminder to consider the type of data being analyzed.
mikemike123
I have 2 problems I am currently stuck on.. one being
In a large sample study according to a report by the U.S. surgeon general, electrical engineers have the lowest smoking rate among all workers surveyed. Only 16% of the male electrical engineers in the sample smoke cigarettes regularly. How many male electrical engineers must be sampled to estimate the proportion of all male electrical engineers who smoke regularly to within 3% of its true value with 95% confidence?

Now for this particular problem I understand they want me to solve for N. In the original equation E=z(alpha/2)* S.D/sqrt(n).. I solved for N and got N=[z(alpha/2)*S.D./E]^2..
So In the problem given, the confidence needed is 95% or .95. Since this is a "large Sample" I assumed using the z table. After looking through it i figured z(alpha/2)=1.96. I would assume E would be .03. This is where i get stuck, there is no S.D given and there is no set of data in the problem so I can not solve for it using the S.D formula. I assume I am interpreting the problem incorrectly. And I am having the same problem with this problem,

In a recent study, 69 of 120 meteorites were observed to enter the Earth's atmosphere with a velocity of less than 26 miles per second.

A) What can you say with 95% confidence about the maximum error?
B) What confidence can we assert that the maximum error of this study is at most 0.055?
C) How large of a sample size is needed if the maximum error of estimate for this study is at most 2.5%

All of these would need a S.D to solve for, or not, I may not be seeing something. Can someone please point me in the right direction.

Thank You.

For the first problem, the number of smokers in the sample would follow the binomial distribution, hence the mean and variance of the observed frequency could be worked out.

For the second problem, need to define "error".

Well in the problem I would assume the mean would be 16% or .16.. how can i solve for a S.D out of this?

Your attack of the first problem isn't correct - think about it: you are dealing with percentages, yet you have the sample size formula based on estimating a mean. you could fudge and use the formula you have, but there is a more direct formula.

similar comment(s) apply to the second problem.

For the more "direct formula", would i use ss = Z^2*(p)*(1-p)/c^2.

So I would have 1.96^2*.16*(1-.16)/.03 which would give me about 574.

I haven't checked your numbers but yes, the formula

$$\widehat p (1-\widehat p) \left(\frac z c\right)^2$$

is the one I was directing you to.

## What is point estimation?

Point estimation is a statistical method used to estimate an unknown population parameter based on a sample of data. This method involves using the sample mean or proportion to estimate the population mean or proportion, respectively.

## What is confidence level?

Confidence level is the probability that the true population parameter falls within a certain range of values. In point estimation, a 95% confidence level means that there is a 95% chance that the true population parameter falls within the estimated range.

## What is a 3% error?

A 3% error in point estimation means that the estimated value could deviate from the true population parameter by up to 3%.

## How is point estimation used in scientific research?

Point estimation is commonly used in scientific research to estimate unknown population parameters, such as the mean or proportion of a certain characteristic in a population. This method allows researchers to make inferences and draw conclusions about a population based on a sample of data.

## What are the limitations of point estimation?

Point estimation relies on the assumption that the sample is representative of the entire population. If the sample is not representative, the estimated value may be biased and not reflect the true population parameter. Additionally, point estimation does not provide information about the precision of the estimate and may not be suitable for small sample sizes.

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