Tests of significance
-
Upload
kerolous-elbogdady -
Category
Engineering
-
view
101 -
download
0
Transcript of Tests of significance
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