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How do you find the sample size if you are given the confidence interval and the margin of error as well as the standard deviation?
Wiki User
∙ 14y ago
You can't. You need an estimate of p (p-hat)
q-hat = 1 - p-hat
variance = square of std dev
sample size n= p-hat * q-hat/variance
yes you can-
it would be the confidence interval X standard deviation / margin of error then square the whole thing
Wiki User
∙ 14y ago
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What is the difference between standard deviation and margin of error?
Standard of deviation and margin of error are related in that they are both used in statistics. Level of confidence is usually shown as the Greek letter alpha when people conducting surveys allow for a margin of error - usually set at between 90% and 99%. The Greek letter sigma is used to represent standard deviation.
What is the relationship between confidence interval and standard deviation?
Short answer, complex. I presume you're in a basic stats class so your dealing with something like a normal distribution however (or something else very standard). You can think of it this way... A confidence interval re-scales margin of likely error into a range. This allows you to say something along the lines, "I can say with 95% confidence that the mean/variance/whatever lies within whatever and whatever" because you're taking into account the likely error in your prediction (as long as the distribution is what you think it is and all stats are what you think they are). This is because, if you know all of the things I listed with absolute certainty, you are able to accurately predict how erroneous your prediction will be. It's because central limit theory allow you to assume statistically relevance of the sample, even given an infinite population of data. The main idea of a confidence interval is to create and interval which is likely to include a population parameter within that interval. Sample data is the source of the confidence interval. You will use your best point estimate which may be the sample mean or the sample proportion, depending on what the problems asks for. Then, you add or subtract the margin of error to get the actual interval. To compute the margin of error, you will always use or calculate a standard deviation. An example is the confidence interval for the mean. The best point estimate for the population mean is the sample mean according to the central limit theorem. So you add and subtract the margin of error from that. Now the margin of error in the case of confidence intervals for the mean is za/2 x Sigma/ Square root of n where a is 1- confidence level. For example, confidence level is 95%, a=1-.95=.05 and a/2 is .025. So we use the z score the corresponds to .025 in each tail of the standard normal distribution. This will be. z=1.96. So if Sigma is the population standard deviation, than Sigma/square root of n is called the standard error of the mean. It is the standard deviation of the sampling distribution of all the means for every possible sample of size n take from your population ( Central limit theorem again). So our confidence interval is the sample mean + or - 1.96 ( Population Standard deviation/ square root of sample size. If we don't know the population standard deviation, we use the sample one but then we must use a t distribution instead of a z one. So we replace the z score with an appropriate t score. In the case of confidence interval for a proportion, we compute and use the standard deviation of the distribution of all the proportions. Once again, the central limit theorem tells us to do this. I will post a link for that theorem. It is the key to really understanding what is going on here!
What Happens To The Width Of The Confidence Interval If You Decrease The Confidence Level Decrease The Sample Size or Decrease the margin of error?
The width of the confidence interval willdecrease if you decrease the confidence level,increase if you decrease the sample sizeincrease if you decrease the margin of error.
In a confidence interval what information does the margin of error provide?
The confidence interval consists of a central value and a margin of error around that value. If it is an X% confidence interval then there is a X% probability that the true value of the statistic in question lies inside the interval. Another way of looking at it is that if you took repeated samples and calculated the test statistic each time, you should expect X% of the test statistics to fall within the confidence interval.
If Web Search Results for A bank wishes to estimate the mean balances owed by their MasterCard customers within 75 The population standard deviation is estimated to be 300 If a 98 percent confidence?
A bank wishing to estimate the mean balances owed by their MasterCard customers within 75 miles with a 98 percent confidence can use the following formula to calculate the required sample size: Sample size = (Z-score)2 * population standard deviation / (margin of error)2 Where Z-score = 2.326 for 98 percent confidence Population standard deviation = 300 Margin of error = desired confidence intervalSubstituting the values into the formula the required sample size is: 2.3262 * 300 / (Confidence Interval)2 = 553.7Therefore the bank would need to have a sample size of 554 to estimate the mean balances owed by their MasterCard customers within 75 miles with a 98 percent confidence.
What happens to the confidence interval as the standard deviation of a distribution increases?
The standard deviation is used in the numerator of the margin of error calculation. As the standard deviation increases, the margin of error increases; therefore the confidence interval width increases. So, the confidence interval gets wider.
How do sample size confidence level and standard deviation affect the margin of error?
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In a poll of 100 adults 45 percent reported they believe in faith healing If the poll was based on 5000 adults would the confidence interval be wider or narrower?
The formula for margin of error is (Z*)*(Standard Deviation))/(sqrt(N)), so as N increases, the margin of error decreases. Here N went from 100 to 5000, so N has increased by 4900. This means the margin of error decreases. Since the confidence interval is the mean plus or minus the margin of error, a smaller margin of error means that the confidence interval is narrower.
How do you find The margin of error for the confidence interval is?
Generally speaking an x% confidence interval has a margin of error of (100-x)%.
What is the difference between standard deviation and margin of error?
Standard of deviation and margin of error are related in that they are both used in statistics. Level of confidence is usually shown as the Greek letter alpha when people conducting surveys allow for a margin of error - usually set at between 90% and 99%. The Greek letter sigma is used to represent standard deviation.
The width of a confidence interval is equal to twice the value of the margin of error?
No. The width of the confidence interval depends on the confidence level. The width of the confidence interval increases as the degree of confidence demanded from the statistical test increases.
What is the relationship between confidence interval and standard deviation?
Short answer, complex. I presume you're in a basic stats class so your dealing with something like a normal distribution however (or something else very standard). You can think of it this way... A confidence interval re-scales margin of likely error into a range. This allows you to say something along the lines, "I can say with 95% confidence that the mean/variance/whatever lies within whatever and whatever" because you're taking into account the likely error in your prediction (as long as the distribution is what you think it is and all stats are what you think they are). This is because, if you know all of the things I listed with absolute certainty, you are able to accurately predict how erroneous your prediction will be. It's because central limit theory allow you to assume statistically relevance of the sample, even given an infinite population of data. The main idea of a confidence interval is to create and interval which is likely to include a population parameter within that interval. Sample data is the source of the confidence interval. You will use your best point estimate which may be the sample mean or the sample proportion, depending on what the problems asks for. Then, you add or subtract the margin of error to get the actual interval. To compute the margin of error, you will always use or calculate a standard deviation. An example is the confidence interval for the mean. The best point estimate for the population mean is the sample mean according to the central limit theorem. So you add and subtract the margin of error from that. Now the margin of error in the case of confidence intervals for the mean is za/2 x Sigma/ Square root of n where a is 1- confidence level. For example, confidence level is 95%, a=1-.95=.05 and a/2 is .025. So we use the z score the corresponds to .025 in each tail of the standard normal distribution. This will be. z=1.96. So if Sigma is the population standard deviation, than Sigma/square root of n is called the standard error of the mean. It is the standard deviation of the sampling distribution of all the means for every possible sample of size n take from your population ( Central limit theorem again). So our confidence interval is the sample mean + or - 1.96 ( Population Standard deviation/ square root of sample size. If we don't know the population standard deviation, we use the sample one but then we must use a t distribution instead of a z one. So we replace the z score with an appropriate t score. In the case of confidence interval for a proportion, we compute and use the standard deviation of the distribution of all the proportions. Once again, the central limit theorem tells us to do this. I will post a link for that theorem. It is the key to really understanding what is going on here!
What Happens To The Width Of The Confidence Interval If You Decrease The Confidence Level Decrease The Sample Size or Decrease the margin of error?
The width of the confidence interval willdecrease if you decrease the confidence level,increase if you decrease the sample sizeincrease if you decrease the margin of error.
In a confidence interval what information does the margin of error provide?
The confidence interval consists of a central value and a margin of error around that value. If it is an X% confidence interval then there is a X% probability that the true value of the statistic in question lies inside the interval. Another way of looking at it is that if you took repeated samples and calculated the test statistic each time, you should expect X% of the test statistics to fall within the confidence interval.
If Web Search Results for A bank wishes to estimate the mean balances owed by their MasterCard customers within 75 The population standard deviation is estimated to be 300 If a 98 percent confidence?
A bank wishing to estimate the mean balances owed by their MasterCard customers within 75 miles with a 98 percent confidence can use the following formula to calculate the required sample size: Sample size = (Z-score)2 * population standard deviation / (margin of error)2 Where Z-score = 2.326 for 98 percent confidence Population standard deviation = 300 Margin of error = desired confidence intervalSubstituting the values into the formula the required sample size is: 2.3262 * 300 / (Confidence Interval)2 = 553.7Therefore the bank would need to have a sample size of 554 to estimate the mean balances owed by their MasterCard customers within 75 miles with a 98 percent confidence.
What are the advantages of a small confidence interval in statistics?
The smaller the confidence interval, the more certain you are of the answers. Remember confidence level and confidence interval (margin of error) are 2 separate things. So if you are using an industry standard confidence level of 95% and 5% margin of error in a standard statistical table, then you could say, for example, with 95% certainty that 60% of those polled would vote for John McCain. Another way of saying this is even though you did not poll everyone (if you did, it would then become a very expensive census), you can say with a high degree of certainty (95% certainty) that 55% to 65% of those polled will vote for Johnny (sadly).
99 percent confidence interval Population mean 24.4 to 38.0 find the mean sample?
if the confidence interval is 24.4 to 38.0 than the average is the exact middle: 31.2, and the margin of error is 6.8
