TEST OF SIGNIFICANCEHypothesis test

CONTENT ▪ Definition of test of significance ▪ Identify the four steps of hypothesis testing▪ State the hypothesis▪ Set criteria for a decision▪ Compute the test statics▪ Make a decision▪ Problem 1▪ Problem 2

TEST OF SIGNIFICANCE• is a method for testing a claim or hypothesis about a parameter in a population, using

data measured in a sample

• For statistical inference, these are predictions about a population expressed in terms of parameters for the variables considered in a study

Treating anorexia, cognitive behavioral and family therapies have same mean weight change as placebo

Mental health tends to be better at higher levels of socioeconomic status (SES)

Spending money on other people has a more positive impact on happiness than spending money on oneself

TEST OF SIGNIFICANCE EXAMPLES

THE METHOD OF HYPOTHESIS TESTING CAN BE SUMMARIZED IN FOUR STEPS

1• State the hypothesis

2• Set criteria for a decision

3• Compute the test statics

4• Make a decision

STEP 1State the hypothesis

Step 1

State the hypotheses

Null hypothesis(H0)

Alternative hypothesis (H1)

Definition :is a statement about a population parameter, such as the population mean, that is assumed to be true.

Example : we state the null hypothesis that engineers in Egypt work an average of 8 hours of work per day

Note :The reason of why we are testing the null hypothesis is because we think it is wrong

Definition:is a statement that directly contradicts a null hypothesis by stating that that the actual value of a population parameter is less than, greater than, or not equal to the value stated in the null hypothesis.

Example :For the engineers working hours example, we may have reason to believe that engineers work more than (>) or less than (<) 8 hours of work per day

EXAMPLE 1▪ Your company hopes to reduce the mean time () required to

process customer orders. At present, this mean is 3.8 days. You study the process and eliminate some unnecessary steps.

to show that the mean is now less than 3.8 days.Target

Ho : μ= 3.8 Ha: μ< 3.8

EXAMPLE 2▪ Experimenters on learning in animals sometimes measure how long it

takes a mouse to find its way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze slower. She measures how long each of 10 mice takes with a noise as stimulus.

H0: =18 Ha: >18

EXAMPLE 3▪ Last year, your company’s service technicians took an average of

2.5 hours to respond to trouble calls from business customers who purchased service contracts. Do this year’s data show a different average response time?

H0: = 2.5 Ha: 2.5

STEP 2Set the criteria for a decision

• we collect data to show that the null hypothesis is not true

• level of significance is typically set at 5% in behavioral research studies

When the probability of obtaining a sample mean is less than 5%

we conclude that the sample we selected is too unlikely and so we reject the null hypothesis

We expect the sample mean to be equal to the population mean

H1 : Engineers work < 8 hours of work per day

H1 : Engineers work > 8 hours of work per day

H1 : Engineers ≠ 8 hours of work per day

µ = 8 µ = 8

µ = 8

Note : that shows us that the alternative hypothesis is used to determine which tail or tails to place the level of significance for a hypothesis test.

STEP 3 Compute the test statistic

The test statistic is a mathematical formula that allows researchers to determine the likelihood of obtaining sample outcomes if the null hypothesis were true

n2

µ = µM

Mean (µ) Standard deviation (z)

npp

pz

/)1(

)p̂(

00

0

STEP 4 Make a decision

MAKE A DECISION

Reject the null hypothesis Retain the null hypothesis

The sample mean is associated with a low proba bility of occurrence when the null hypothesis is true

The sample mean is associated with a high proba bility of occurrence when the null hypothesis is true.

PROBLEM 1الماضي العام في وسجل التروس صناديق النتاج انتاج% 5مصنع

الكلي االنتاج من .معيب

عينة أخذ فتم الجديد العام في المصنع مستوي تحديد المصنع وأرادn= 1000 العينة في المنتجات عدد وكان

بهم , 30وجد وما , ال ام أداه تحسن المصنع كان إذا حدد معيب منتجحدث؟ الذي التغير مقدار

STEP 1: FORMULATE HYPOTHESIS

New Sample proportion = 30/1000 = 0.03

So: 0.03<0.05

H0: P = 0.05 - HA: P ≠ 0.05

Step 2: Set criteria for a decision

STEP 3: CALCULATE Z IN DATA

1000/)05.01(05.0

)05.003(.

/)1(

)p̂(

00

0

npp

pz

3.3z

Step 4 : Make a decisionWe expect the sample mean to be

equal to the population mean

H1 : Calculated defect <expected defect

H1 : calculated defect ≠ expected defect

µ = .05 µ = .05

µ = .05

H1 : calculated defect > expected defect

We expect the sample mean to be equal to the population mean

H1 : calculated defect < expected defect

µ = .05

Z = +3.3Z= 0Z= -3.3

A1

A2

Step 4 : Make a decision

Area under the curve

Step 4 : Make a decisionCalculate changing percentage

Percentage= Area under the curve = A1 – A2 = 0.5 - .00043 = .49957

باعمال الفنيين قام المنتاجات لنقل سير يوجد االنتاج مصانع باحدينقل الصيانة عملية قبل السير وكان به الساعة 900صيانة في منتج

لـ السير نقل نقل 920ومتوقع معدل ان العلم مع الساعة في منتجقبل , 1000السير النقل نسبة ما الجديدة حالته في الساعة منتج

االفتراضي؟ االختبار نتيجة وما الصيانة وبعد

PROBLEM 2

STEP 1: FORMULATE HYPOTHESIS

New Sample proportion = 920/1000 = 0.92

So: 0.92>0.9

H0: P = 900/1000=0.9 - HA: P > 0.9

Step 2: Set criteria for a decision

STEP 3: CALCULATE Z IN DATA

1000/)9.01(9.0

)9.092.0(

/)1(

)p̂(

00

0

npp

pz

1.2z

Step 4 : Make a decisionWe expect the sample mean to be

equal to the population mean

H1 : Calculated transportation rate <expected transportation rate

H1 : calculated transportation rate ≠ expected transportation rate

µ = .9 µ = .9

µ = .9

H1 : calculated transportation rate > expected

transportation rate

We expect the sample mean to be equal to the population mean

µ = .9

Z = +2.1Z= 0Z= -2.1

A1

A2

Step 4 : Make a decision

Area under the curve

H1 : calculated transportation rate > expected

transportation rate

Step 4 : Make a decisionCalculate changing percentage

Percentage= Area under the curve = A2 – A1 = 0.9821 – 0.5 = 0.4821

PRESENTED BY Kerolos Amin Farahat

Mostafa Saaid Abas