Please be prepared to have exercises every class meeting

This means bringing your formula sheets, statistics tables and calculators EVERY MEETING

Exercises every class meeting will be offsetting quizzes for this part of IE 27

Today’s Agenda:

Hypothesis Testing

HAVE YOU EVER BEEN REJECTED?

#AWTSU

HypothesisTesting

Parameter Estimation

We are guessing the true value of a

parameter using a test statistic either by

giving an exact value (Point Estimation) or a

range of values (Confidence Intervals)

Hypothesis Testing

Given an initial guess of the true value of a

parameter we will test whether that guess is

correct

HypothesisTesting

The uses of Hypothesis Testing

Whether to accept a statistical hypothesis

To test the statistical significance of a certain value

HypothesisTesting

You are given the Third exam scores of 10 randomly selected IE 27 students. Test if the mean score for the third long exam is

eqaul to the passing rate (μ = 56)

The average exam score (Xbar) is a random variable

The average exam score (Xbar) is also a sample statistic

In hypothesis testing we also call a sample statistic as a TEST STATISTIC as it will be used to test the hypothesis

Our Hypothesis (Ho) is that the mean score of 46 students is equal than 56 (Ho: μ = 56)

HypothesisTesting

You are given the Third exam scores of 10 randomly selected IE 27 students. Test if the mean score for the third long exam is

passing (μ = 56)

In Hypothesis Testing we create two hyoptheses

Null Hypothesis

Ho: μ = 56

Alternative Hypothesis

H1: μ ≠ 56

We are sure that only ONE of these is true

HypothesisTesting

You are given the Third exam scores of 10 randomly selected IE 27 students. Test if the mean score for the third long exam is

passing (μ = 56)

Null Hypothesis

Ho: μ = 56

Alternative Hypothesis

H1: μ ≠ 56

In Hypothesis Testing we either, REJECT THE NULL HYPOTHESIS or FAIL TO REJECT THE NULL HYPOTHESIS at a certain level of

significance

We do not say that we “Accept the Null Hypothesis” because at a certain level of significance it may lead us to reject the null

hypothesis

REJECTION IS SUCH A STRONG CONCLUSION…at alam naman nating masakit mareject

HypothesisTesting

You are given the Third exam scores of 10 randomly selected IE 27 students. Test if the mean score for the third long exam is

passing (μ = 56)

Null Hypothesis

Ho: μ = 56

Alternative Hypothesis

H1: μ ≠ 56

In hypothesis testing, a rejection region is computed and the test statistic is compared

HypothesisTesting

Type I Error (Alpha Error)Rejecting the null hypothesis when the null

hypothesis is actually true

Type II Error (Beta Error)

Accepting the null hypothesis when the null hypothesis is actually fallse

HypothesisTesting

ARTBAF

lpha

eject when

rue

eta

ccept when

alse

DecisionHo is True

Ho is False

Reject HoType I Error no error

Fail to reject Ho

no error Type II Error

HypothesisTesting

Decision Mr./Ms. Right Mr./Ms. Right Now

Pinakawalan mo Type I Error no error

Kayo na Forever no error Type II Error

Decision Student is good Student is bad

Fail a student Type I Error no error

Pass a student no error Type II Error

HypothesisTesting

Type I Error

Suppose this is the distribution of the true population mean μ = 60

Suppose we set that α = 5%, thus the corresponding critical region is as follows

In hypothesis testing, a is set by the analyst

HypothesisTesting

Type II Error

Suppose this is the distribution of the true population mean μ = 63

Suppose the critical values are 57.5 and 62.5, we do not reject Ho if the sample statistic is within those limits

But Ho states that μ = 60

HypothesisTesting

Analyzing Type I & II Error

Unlike Alpha, Beta is dependent on the true mean of the parameter

Since the probability of not rejecting the null hypothesis is not set by the analyst but a function of both the sample size and the critical values, the acceptance of the null hypothesis is a

weak conclusion

HypothesisTesting

Analyzing Type I & II Error

If the critical region becomes smaller, the probability of Type I Error, alpha, reduces

HypothesisTesting

Analyzing Type I & II Error

If the true value of the parameter approaches the value hypothesized in the null hypothesis, the probability of Type II

Error, beta, increases

If the difference between the true mean and hypothesized value increases, the probability of Type II Error, beta, decreases

HypothesisTesting

Analyzing Type I & II Error

If we increase sample size, the sample distribution tends to approach the population distribution

If we increase sample size and retain confidence level, both alpha and beta reduces (more accurate, less error)

HypothesisTesting

Analyzing Type I & II Error

If only one of the null and alternative hypothesis is correct, it means the error associated with them are related

If sample size is constant, an increase in the probability of one type of error results in a decrease in the probability of

the other

HypothesisTesting

Power of a Statistical testCorrectly rejecting the null hypothesis when

it is false

Power = 1 – β

A statistical test with higher power is desired. Increasing sample size or increasing

alpha will result to a higher powered test

Power is the probability to “detect” whether a hypothesized value is really far from the

true value

HypothesisTesting

General Procedure for Hypothesis testing

Determine the Parameter of InterestStep 1:

State the Null HypothesisStep 2:

State the Alternative HypothesisStep 3:

Determine AlphaStep 4:

Determine Test StatisticStep 5:

Determine Rejection RegionStep 6:

Compute Test StatisticStep 7:

ConcludeStep 8:

Sourc: Taha

Next Time on IE 27

Solving Hypothesis testing

.Fin.