Question

How is the Confidence Interval important to business leaders?

How is the Margin of Error Useful?

When is the Central Limit Theorem used by businesses How do researchers define a Sample Size?

What does the P-Value mean and how is it used by businesses and researchers ?

Why is Hypothesis Testing useful?

Answer 1

a)

Confidence Intervals.

confidence interval gives the percentage probability that an estimated range of possible values in fact includes the actual value being estimated.

For example, a business might estimate that a machine uses 10 lbs. of plastic for each unit of a product created

Because the machine cannot be expected to use precisely 10 lbs. per unit

a confidence interval can be created to give a range of possibilities

. The company might predict that there is a 95 percent chance that the machine uses on average between 9.85 and 10.5 lbs. of plastic per unit.

The confidence interval in this example is 95 percent, and the likelihood that the actual amount of plastic used is outside the estimated range is 5 percent.

It is useful in market research ,Risk management and budget forecasting

Budget forecasting:

When a business leader forecasts a budget for a fiscal period,

it will need to estimate both revenues and costs.

If a company is significantly off the mark on either estimation, it could get in financial trouble.

By using a range of possible values for revenues and costs and finding the confidence interval of those values, a business can have the information it needs to make important financial decisions while still being able to reasonably prepare for the possibility that its estimates may be incorrect

b)

The margin of error determines how reliable the survey is or how reliable the results of the experiment are.​​​​​​

Any survey takes a sample population from the whole population and then generalizes the results to the whole population. This invariably leads to a possibility of error because the whole can never be accurately described by a part of it.

In statistics margin of error is related to the confidence interval as being equal to half the interval length. This means higher the confidence interval, higher the margin of error for the same set of data. This is expected because to get a higher confidence interval, one usually needs higher data points. It is also quite expected that as the number of samples increases, the margin of error decreases

c)

We will use the central limit theorem in financial market,Quality control

Financial market :

Suppose that we are assembling a portfolio of stocks or other financial holdings and want to balance the overall risk against the possible rewards. We can help make that assessment by using the central limit theorem and our knowledge of the patterns found in normal distributions.

One way to approach this issue would be to consider how individual sectors of the economy have performed during various business cycles, and incorporate that information into our investment model. We know that the returns for each sector might be quite variable over time. However, using the historical data, we can repeatedly take samples from each sector during various overall market cycles, and find the associated mean value for each sector.

In doing so, the central limit theorem states that we will create a good approximation of each sector's average return, along with a normal distribution of those sample average

Quality Control:

Quality control is an important consideration in many businesses. In some production systems the number of variables that can affect the overall quality of a product may seem overwhelming. How can we control for temperature, pressure, machine tolerance,difference in raw material,human error

According to central limit theorem individual contributions to the quality measurement have same relative effect

Then their cumulative effect will follow the normal distribution data

Central limit theorem also helps when setting the sampling guidelines

It is very important to determine the proper or accurate sample size in any field of research.

Sometimes researchers cannot take the decision that how many number of individuals or objects will they select for their study purpose. Also, a set of survey data is used to verify that central limit theorem (CLT) for different sample sizes.

From the data of 1348 students we got the average weight for our population of BRAC University students is 62.62 kg with standard deviation 11.79 kg.

We observed that our sample means became better estimators of true population mean. In addition, the shape of the distribution became more Normal as the sample size increased.

So it is concluded that our simulation results were consistent with central limit theorem

d)

P values evaluate how well the sample data support the devil’s advocate argument that the null hypothesis is true. It measures how compatible your data are with the null hypothesis. How likely is the effect observed in your sample data if the null hypothesis is true?

High P values: your data are likely with a true null.

Low P values: your data are unlikely with a true null.

A low P value suggests that your sample provides enough evidence that you can reject the null hypothesis for the entire population

e)

hypothesis testing is one of the most important concepts in statistics because

it is how you decide if something really happened, or if certain treatments have positive effects, or if groups differ from each other or if one variable predicts another.

In short, you want to proof if your data is statistically significant and unlikely to have occurred by chance alone. In essence then, a hypothesis test is a test of significance.