Type i and ii errors, Applied Statistics

Assignment Help:

TYPE I AND II Errors

If a statistical hypothesis is tested, we may get the following four possible cases:

  1. The null hypothesis is true and it is accepted;

  2. The null hypothesis is false and it is rejected;

  3. The null hypothesis is true, but it is rejected;

  4. The null hypothesis is false, but it is accepted.

Clearly, the last two cases lead to errors which are called errors of sampling. The error made in (c) is called Type I Error. The error committed in (d) is called Type II Error. In either case a wrong decision is taken.

P(Committing a Type I Error)

=       P (The Null Hypothesis is true but is rejected)\

=       P (The Null Hypothesis is true but sample statistic falls in the rejection region)

=    α, the level of significance

P(Committing a Type II Error)

=       P (The Null Hypothesis is false but sample statistic falls in the acceptance 
         region)

=        β (say)

The level of significance,   α , is known. This was fixed before testing started.   β is known only if the true value of the parameter is known. Of course, if it is known, there was no point in testing for the parameter.


Related Discussions:- Type i and ii errors

Statistical generalisations, From the information given, what seems to be t...

From the information given, what seems to be the main flaw in each of the following statistical generalisations? (i) Banking industry employees are facing a crisis, if their

Distribution of sample means, 1. Use the concepts of sampling error and z-s...

1. Use the concepts of sampling error and z-scores to explain the concept of distribution of sample means. 2. Describe the distribution of sample means shape for samples of n=36

Managerial report, A. Compute descriptive statistics for each stock and the...

A. Compute descriptive statistics for each stock and the S&P 500. Comment on your results. Which stocks are most volatile?

Correlation coefficient test, 1. If you are calculating a correlation coeff...

1. If you are calculating a correlation coefficient testing the relationship between height and weight, state the null and alternative hypotheses. 2. What kind of relationship d

Sampling theory, difference between large sample test and small sample test...

difference between large sample test and small sample test

Probability and expectation, Ten balls are put in 6 slots at random.Then ex...

Ten balls are put in 6 slots at random.Then expected total number of balls in the two extreme slots

Accident proneness, Accident proneness  A personal psychological issue w...

Accident proneness  A personal psychological issue which affects the individual's probability of suffering the accident. The concept has been studied statistically under the num

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd