3. Confidence Interval Estimation

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Do curso por University of London

Statistics for International Business

121 classificações

University of London

Statistics for International Business

121 classificações

Curso 4 de 6 em 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

Conheça os instrutores

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

[MUSIC]

A confidence interval estimator for a population parameter is a rule for

individuating an interval in which it is likely to find the parameter of interest.

The estimate is called a confidence interval estimate.

Therefore, the aim of the confidence interval estimator is to find the range

of values, rather than a single number in order to estimate a population mean.

This is possible because sometimes happens that similar populations

have been sampled very often and

the variance of the interested populations can be assumed,

known to a very close approximation based on the past experience.

Also, when the sample size n gets larger,

we estimate the population variance from the sample by

applying the same procedure we use when the variance is known.

In sampling from a population, all other things being equal,

we have more information about the population if we work

with a relatively large sample than it would be if working with a smaller sample.

However, this factor is not reflected in a point estimates.

Increased precision in the information is reflected in confidence

interval estimates.

In fact, all other things being equal,

the larger the sample size, the narrower the interval estimates.

And then, the less the uncertainty on the true value of the parameter.

Suppose that we have a random sample, and

we find two random variables, C and D, with C less than D.

Suppose now that the specific sample values of the random variables C and

D are c and d.

The interval which goes from C to D, may include or may not,

the parameter we are interested in.

We cannot be sure about it.

However, if we take random samples for

repeated times from the population, and

we find similar intervals, in the long run a certain

percentage of these intervals, such as 95%, or 98%,

will contain the true value of the unknown parameter.

The interval from c to d is indicated to be

a 95% confidence interval estimator for the population proportion.

If beta is the unknown parameter,

suppose that we find the random variables C and D,

such that the probability that beta is in between C and

D is equal to 1 minus alpha.

Where alpha is any number between zero and one.

If the specific sample values of C and D are c and d,

then the interval from C to D is 100 times

1 minus alpha percent, confidence interval of beta.

The quantity 100(1-

alpha)% is the confidence level of the interval.

If we sample the population for a large number of times,

the true value of the parameter beta will be covered by 100

times 1 minus alpha percent of intervals.

The confidence interval calculated is indicated as b between c and

d, with 100 times 1 minus alpha percent confidence.

[MUSIC]

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