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Neporo4naja [7]
3 years ago
12

13. Interpret the phrase ""margin of sampling error is ±1 percentage point.""

Mathematics
1 answer:
Ulleksa [173]3 years ago
4 0

Answer:

On this case a margin of error of \pm 1 \% means that the true population proportion is 1% above or below the estimated proportion calculated from the sample. And this value helps in order to find the limits for a confidence interval with a confidence given.  

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Solution to the problem

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

On this case a margin of error of \pm 1 \% means that the true population proportion is 1% above or below the estimated proportion calculated from the sample. And this value helps in order to find the limits for a confidence interval with a confidence given.  

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Step-by-step explanation:

When you ask, "What is 55.5 as a decimal?", we assume you want to know what 55.5 percent is as a decimal. In other words, 55.5 percent converted to decimal.

First, we will tell you why it is useful to know 55.5 as a decimal.

Normally, to calculate 55.5 percent, you would multiply a number by 55.5 percent and then you would take the product of that and divide it by 100 to get the answer.

Instead, you can simply multiply a number by 55.5 as a decimal to get the answer.

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