Question

In a short paragraph, distinguish between Sampling Error and the Margin of Error. Explain what each represents and the relationship between them. (3 points)

In a short paragraph, distinguish between a Point Estimate and an Interval Estimate. Explain what each represents and the relationship between them. (3 points)

TYPED ONLY PLEASE!!!!

Answer 1

Hi, i hope you'll find my answe very helpful, Please LIKE it, Thanks.

A sampling error is a statistical error that occurs when an analyst does not select a sample that represents the entire population of data and the results found in the sample do not represent the results that would be obtained from the entire population. Sampling is an analysis performed by selecting a number of observations from a larger population, and the selection can produce both sampling errors and non-sampling errors.

• Sampling error is a statistical error that occurs when an analyst does not select a sample that represents the entire population of data.
• The results found in the sample thus do not represent the results that would be obtained from the entire population.
• Sampling error can be reduced by randomizing sample selection and/or increasing the number of observations.

Whereas,

A margin of error tells you how many percentage points your results will differ from the real population value. For example, a 95% confidence interval with a 4 percent margin of error means that your statistic will be within 4 percentage points of the real population value 95% of the time.

More technically, the margin of error is the range of values below and above the sample statistic in a confidence interval. The confidence interval is a way to show what the uncertainty is with a certain statistic (i.e. from a poll or survey).

For example, a poll might state that there is a 98% confidence interval of 4.88 and 5.26. That means if the poll is repeated using the same techniques, 98% of the time the true population parameter (parameter vs. statistic) will fall within the interval estimates (i.e. between 4.88 and 5.26) 98% of the time.

Now,

In Parametric Statistics, one common goal is to estimate the [unknown] parameter(s) of some population (or distribution).

There are countless techniques to approach that.

However, 2 main categories of techniques are, as you mention, point estimation and interval estimation.

The first category, point estimation, gives you a “punctual” answer to the problem of parameter estimation, by suggesting a unique value. The value is usually found by instantiating functions which, in the space of all possible samples, ensure some “desirable” statistical property (consistency, efficiency, unbiasedness)/.

Interval estimation, instead, suggests an interval that might contain the unknown value, and also provides an evaluation of the “level of confidence” we can have that the actual value is actually in the interval.

• Point estimate. A point estimate of a population parameter is a single value of a statistic.

For example, the sample mean x is a point estimate of the population mean μ. Similarly, the sample proportion p is a point estimate of the population proportion P.

• Interval estimate. An interval estimate is defined by two numbers, between which a population parameter is said to lie.

For example, a < x < b is an interval estimate of the population mean μ. It indicates that the population mean is greater than a but less than b.

That’s it, I hope ypu understood my answer. Please do like it, Thanks.