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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.

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โˆ™ 2013-05-22 22:16:58
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Q: What is the difference between standard deviation and margin of error?
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A random sample of 120 students has a test score average with a standard deviation of 11.4 Find the margin of error if c equals 0.90?

i y=use Z-test


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?

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


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!


Why does the margin of error increase as the confidence increases?

The margin of error is dependent on the confidence interval.I'll give you examples to understand it better.We know:Confidence Interval (CI) = x(bar) ± margin of error (MOE)MOE = (z confidence)(sigma sub x bar, aka standard error of mean)When CI = 95%, MOE = (1.96)(sigma sub x bar)When CI = 90%, MOE = (1.64)(sigma sub x bar)Naturally, the margin of error will decrease as confidence level decreases.


How does sample size affect the margin of error?

The larger the sample size, the smaller the margin of error.

Related questions

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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Rolling margin of steel rod which is used for construction?

Rolling Margin is the deviation of actual unit weight to that of Standard unit weight as per IS Standards. Rolling Margin is calculated as : Sectional weight = Weight of Steel Bars dia wise / length of the bars. As per IS Standards unit weight of the Bars is calculated as dia x dia / 162 Rolling Margin is deviation of actual sectional weight to that of IS Standard unit weight. Standard Rolling Margin for different dia reinforcement bars used for construction purposes: 8mm to 10mm +- 7% 12mm to 16mm +- 5% 20mm & Above +- 3%


What is an example sentence for leeway?

The permissible margin for variation or deviation from something.


What is the difference between margin trading and credit given by stock brokers?

Credit given by stockbrokers IS margin trading.


What is the difference between net and gross margin?

Gross margin is Gross income as a percentage of revenue. Net Margin is net income as a percentage of revenue.


A random sample of 120 students has a test score average with a standard deviation of 11.4 Find the margin of error if c equals 0.90?

i y=use Z-test


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?

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


What is Confidence Intervals of Margin of Error?

The magnitude of difference between the statistic (point estimate) and the parameter (true state of nature), . This is estimated using the critical statistic and the standard error.


What is a reasonable profit margin?

what is the difference between reasonable profits and economic profits


How is a margin determined?

There are different kinds of margin. In printing, a margin is the distance between the edge of a physical page and where on the page the printing is. In business the margin is the difference between the market value of a stock and the loan a broker makes. A profit margin is calculated by finding the net profit as a percentage of the revenue.


What is the difference between Contribution Margin per unit and contribution margin ratio?

Contribution margin ratio is overall total contribution margin while contribution margin ration per unit is the allocation of total production contribution margin to per unit basis.

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