3.1 Confidence Intervals, Part 2

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En provenance du cours de University of London

Statistics for International Business

110 notes

University of London

Statistics for International Business

110 notes

Cours 4 sur 6 dans Specialization International Business Essentials

This course introduces core areas of statistics that will be useful in business and for several MBA modules. It covers a variety of ways to present data, probability, and statistical estimation. You can test your understanding as you progress, while more advanced content is available if you want to push yourself. This course forms part of a specialisation from the University of London designed to help you develop and build the essential business, academic, and cultural skills necessary to succeed in international business, or in further study. If completed successfully, your certificate from this specialisation can also be used as part of the application process for the University of London Global MBA programme, particularly for early career applicants. If you would like more information about the Global MBA, please visit https://mba.london.ac.uk/. This course is endorsed by CMI

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Statistical Estimation

For statistical analysis to work properly, it’s essential to have a proper sample, drawn from a population of items of interest that have measured characteristics. This week, we will cover statistical estimation, sampling distribution of the mean, point estimation, interval estimation, hypothesis testing, the Null hypothesis and look at some real life examples of their use.

Statistical Estimation - An Introduction7:27

1. Statistical Estimation0:47

2. Estimator and Estimate1:47

2.1. Point Estimator and Point Estimate1:41

2.2. Unbiased2:30

2.3. Efficiency2:25

3. Confidence Interval Estimation4:46

3.1 Confidence Intervals, Part 112:44

3.1 Confidence Intervals, Part 24:16

4. Testing Hypothesis2:40

4.1. Formulation of the Null Hypothesis and the Alternative Hypothesis3:34

4.2. Test Statistic0:56

4.2.1. The Decision Rule2:10

4.2.2. Types of Errors1:48

4.2.3. Performing the Test and the Decision Rule3:22

4.2.3.1 Hypothesis Testing: Examples7:59

5. Regression Model5:07

Statistical Estimation - Summary3:15

Rencontrer les enseignants

George Kapetanios
Professor of Finance and Econometrics
King's College London

[MUSIC]

Let's get back to the example of cereals.

We are looking for mu.

What we know, We know

that based on the sample that we have, the average weight of

30 packs of cereals would be 30, it's 301.5 grams.

We have to add one piece of information here.

The piece of information, as you could already imagine from before,

was that we were missing this bit.

Which is the actual variants of the population, in terms of gram.

So let's assume it's just 1 gram,

we also were told that we're talking about 95% confidence.

So let's try to plug back in the values.

So we said that the mu,

with 95% confidence,

will be 301.5 grams plus minus

1.96 1 over square root of 30.

In other words, we can say that, with 95% confidence,

we can say that mu will be in this region.

So let's try to calculate the upper and

the lower bound of this confidence interval.

So the upper bound,

that's called the upper bound of mu,

will be 301.5 + 1.96 1 over 300,

which will be equal to 301.86.

The lower bound of this mu will be

301.5- 1.96 1 over 30,

which will be 301.14.

So if you want to picture this, if this is our confidence interval,

the x upper bar will be always in the middle,

301.5 grams.

This is our mean, the sample mean.

The lower bound will be 301.4 grams and

the upper bound is 301.86 grams.

So what we can say that with 95% confidence,

we know that our mean of all the population,

of all the cereal boxes that is produced by this manufacturer,

will be definitely above this 300 grams that are advertised on the box.

Now, it's very important to produce this kind of information because

from consumer perspective, it will be important that the consumers will

have the correct information on the boxes.

So if, with 95% confidence, we can say that the cereal boxes,

all the cereal boxes, produced by this manufacturer are above 300 grams,

then I would be suspecting that consumers will not complain.

However, if we find that with 95% confidence,

this is below 300 grams, then the producer has a problem that it may face

legal suits against himself or herself in those situations.

So the statistic information that is encoded within the confidence

interval will be quite important to this kind of producer.

[MUSIC]

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