SPSS does not have Z test for proportions, So, we use Chi-Square test for proportion tests. Test for single proportion and Test for proportions of two samples
Chi-Square test for independence of attributes / Chi-Square test for checking association between two categorical variables, Chi-Square test for goodness of fit
Normal Distribution – Introduction and PropertiesSundar B N
In this video you can see Normal Distribution – Introduction and Properties.
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Chi-Square test for independence of attributes / Chi-Square test for checking association between two categorical variables, Chi-Square test for goodness of fit
Normal Distribution – Introduction and PropertiesSundar B N
In this video you can see Normal Distribution – Introduction and Properties.
Watch the video on above ppt
https://www.youtube.com/watch?v=ocTXHLWsec8&list=PLBWPV_4DjPFO6RjpbyYXSaZHiakMaeM9D&index=4
Subscribe to Vision Academy
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Research methodology - Estimation Theory & Hypothesis Testing, Techniques of ...The Stockker
Fundamentals, Standard Error, Estimation, Interval Estimation, Hypothesis, Characteristics of Hypothesis, Testing The Hypothesis, Type I & Type II error, One tailed & Two tailed test, Tabulated Values, Chi-square (2) Test, Analysis of variance (ANOVA)Introduction, The Sign Test, The rank sum test or The Mann-Whitney U test, Determination of Sample Size
Inferential statistics takes data from a sample and makes inferences about the larger population from which the sample was drawn.
Make use of the PPT to have a better understanding of Inferential statistics.
Basics of Hypothesis testing for PharmacyParag Shah
This presentation will clarify all basic concepts and terms of hypothesis testing. It will also help you to decide correct Parametric & Non-Parametric test for your data
[The following information applies to the questions displayed belo.docxdanielfoster65629
[The following information applies to the questions displayed below.]
A sample of 36 observations is selected from a normal population. The sample mean is 12, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.01 significance level.
H0: μ ≤ 10
H1: μ > 10
1.
Value:
10.00 points
Required information
a.
Is this a one- or two-tailed test?
One-tailed test
Two-tailed test
References
EBook & Resources
Multiple Choice Difficulty: 2 Intermediate Learning Objective: 10-05 Conduct a test of a hypothesis about a population mean.
eBook: Conduct a test of a hypothesis about a population mean.
Check my work
2.
Value:
10.00 points
Required information
b.
What is the decision rule?
Reject H0 when z ≤ 2.326
Reject H0 when z > 2.326
References
EBook & Resources
Multiple Choice Difficulty: 2 Intermediate Learning Objective: 10-05 Conduct a test of a hypothesis about a population mean.
eBook: Conduct a test of a hypothesis about a population mean.
Check my work
3.
Value:
10.00 points
Required information
c.
What is the value of the test statistic?
Value of the test statistic
References
EBook & Resources
Worksheet Difficulty: 2 Intermediate Learning Objective: 10-05 Conduct a test of a hypothesis about a population mean.
eBook: Conduct a test of a hypothesis about a population mean.
Check my work
4.
Value:
10.00 points
Required information
d.
What is your decision regarding H0?
Fail to reject H0
Reject H0
References
EBook & Resources
Multiple Choice Difficulty: 2 Intermediate Learning Objective: 10-05 Conduct a test of a hypothesis about a population mean.
eBook: Conduct a test of a hypothesis about a population mean.
Check my work
5.
Value:
10.00 points
Required information
e.
What is the p-value?
p-value
References
Given the following hypotheses:
H0 : μ = 400
H1 : μ ≠ 400
A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using the .01 significance level:
a.
State the decision rule. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.)
Reject H0 when the test statistic is the interval (,).
b.
Compute the value of the test statistic. (Round your answer to 3 decimal places.)
Value of the test statistic
c.
What is your decision regarding the null hypothesis?
Do not reject
Reject
The management of White Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using the .10 level of significance, can we conclude that the assembly time using the new method is faster?
a.
What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Rej.
This will help understand the basic concepts of Statistics like data types, level of measurements, central tendency, dispersion, graphs, univaraite analysis, bivariate analysis and more. Moreover, it will also help you to select appropriate summary statistics and charts for your data.
Non-parametric tests are sometimes called distribution-free tests because they are based on fewer assumptions (e.g., they do not assume that the outcome is approximately normally distributed). The cost of fewer assumptions is that non-parametric tests are generally less powerful than their parametric counterparts.
Correlation & Regression Analysis using SPSSParag Shah
Concept of Correlation, Simple Linear Regression & Multiple Linear Regression and its analysis using SPSS. How it check the validity of assumptions in Regression
Chi Square test for independence of attributes / Testing association between two categorical variables, Chi-Square test for Goodness of fit / Testing significant difference between observed and expected frequencies
t test for single mean, t test for means of independent samples, t test for means of dependent sample ( Paired t test). Case study / Examples for hands on experience of how SPSS can be used for different hypothesis testing - t test.
Exploratory Data Analysis for Biotechnology and Pharmaceutical SciencesParag Shah
This presentation will give perfect understanding of data, data types, level of measurements, exploratory data analysis and more importantly, when to use which type of summary statistics and graphs
This presentation will clarify all your basic concepts of Probability. It includes Random Experiment, Sample Space, Event, Complementary event, Union - Intersection and difference of events, favorable cases, probability definitions, conditional probability, Bayes theorem
This ppt includes basic concepts about data types, levels of measurements. It also explains which descriptive measure, graph and tests should be used for different types of data. A brief of Pivot tables and charts is also included.
The ppt gives an idea about basic concept of Estimation. point and interval. Properties of good estimate is also covered. Confidence interval for single means, difference between two means, proportion and difference of two proportion for different sample sizes are included along with case studies.
Testing of hypothesis - large sample testParag Shah
Different type of test which are used for large sample has been included in this presentation. Steps for each test and a case study is included for concept clarity and practice.
This ppt is to guide students opting for Statistics major. It gives an idea of skills required and job prospects. It also emphasizes on the important life skills along with Statistics knowledge, analytical thinking and hands on analytical software .
Techniques to optimize the pagerank algorithm usually fall in two categories. One is to try reducing the work per iteration, and the other is to try reducing the number of iterations. These goals are often at odds with one another. Skipping computation on vertices which have already converged has the potential to save iteration time. Skipping in-identical vertices, with the same in-links, helps reduce duplicate computations and thus could help reduce iteration time. Road networks often have chains which can be short-circuited before pagerank computation to improve performance. Final ranks of chain nodes can be easily calculated. This could reduce both the iteration time, and the number of iterations. If a graph has no dangling nodes, pagerank of each strongly connected component can be computed in topological order. This could help reduce the iteration time, no. of iterations, and also enable multi-iteration concurrency in pagerank computation. The combination of all of the above methods is the STICD algorithm. [sticd] For dynamic graphs, unchanged components whose ranks are unaffected can be skipped altogether.
Explore our comprehensive data analysis project presentation on predicting product ad campaign performance. Learn how data-driven insights can optimize your marketing strategies and enhance campaign effectiveness. Perfect for professionals and students looking to understand the power of data analysis in advertising. for more details visit: https://bostoninstituteofanalytics.org/data-science-and-artificial-intelligence/
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2. TEST FOR PROPORTION(S)
There are mainly two tests for proportion
• Test for single proportion
• Test for significant difference between proportion of two samples
SPSS does not have Z test to test the proportion(s).
But Chi-Square test can be used to the test the proportion in SPSS.
3. Chi- Square Statistic
If X~𝑁(𝜇, 𝜎2) then 𝑍 =
𝑋−𝜇
𝜎
~𝑁(0,1) and
𝑍2
=
𝑋−𝜇
𝜎
2
~𝜒2
with 1 d.f. and
𝑋−𝜇
𝜎
2
~𝜒2
with n d.f.
4. Test of Single
Proportion
Step 1: Null hypothesis H0: 𝑃 = 𝑃0
Step 2: Alternative hypothesis H1: 𝑃 ≠ 𝑃0 or 𝑃 > 𝑃0 or 𝑃 < 𝑃0
Step 3: Test statistics
𝑧 =
𝑝 −𝑃0
𝑃0 ∗𝑄0
𝑛
Denominator is the Standard Error of sample proportion i.e. S.E.(𝑝)
Step 4: Table value of z at 𝛼 % level of significance
Step 5: If z ≤ z table value, H0 is Accepted
If z > z table value, H0 is Rejected
5. Test of Single
Proportion
Step 1: Null hypothesis H0: 𝑃 = 𝑃0
Step 2: Alternative hypothesis H1: 𝑃 ≠ 𝑃0 or 𝑃 > 𝑃0 or 𝑃 < 𝑃0
Step 3: Check Assumptions
Step 4: Test statistic – Chi-square and p value
Step 5: Conclusion
• If p ≤ Level of significance (∝), We Reject Null hypothesis
• If p > Level of significance (∝), We fail to Reject Null hypothesis
6. Case Study
The CEO of a large water pump manufacturing company claims that more than 80 percent of
his customers are satisfied with the water pump. To test this claim, the local newspaper
surveyed 100 customers, using simple random sampling. Among the sampled customers, 73
percent say they are very satisfied. Based on these findings, what can we say about the
manufacturer’s claim ? Use a 0.05 level of significance.
7. Null & Alternative
Hypothesis
Step 1: H0: P = 0.80
[Not more than 80% of the customers are satisfied ]
Step 2: H1: P > 0.80
[More than 80% of the customers are satisfied ]
(One-tailed test)
8. Data in SPSS
The local newspaper
surveyed 100 customers,
using simple random
sampling. Among the
sampled customers, 73
percent say they are very
satisfied
12. Output
The Chi-square value is 3.063 and
p value = (0.080)/ 2 = 0.04
As p < 0.05, We reject the Null hypothesis.
∴ More than 80% of the customers are
satisfied
𝑧 =
𝑝 −𝑃
𝑃∗𝑄
𝑛
=
0.73 −0.80
0.80∗0.20
100
= 1.75
Chi-Square = Square of z value
13. Test of significance of difference between two proportions
Step 1: Null hypothesis H0: 𝑃1= 𝑃2
Step 2: Alternative hypothesis H1: 𝑃1 ≠ 𝑃2 or 𝑃1 > 𝑃2 or 𝑃1 < 𝑃2
Step 3: Test statistics
𝑧 =
𝑝1 − 𝑝2
𝑃1∗𝑄1
𝑛1
+
𝑃2∗𝑄2
𝑛2
or
𝑝1 − 𝑝2
𝑃∗𝑄 (
1
𝑛1
+
1
𝑛2
)
where 𝑃 =
𝑛1𝑝1+𝑛2𝑝2
𝑛1+𝑛2
Denominator is the Standard Error of difference in sample proportion i.e. S.E.(𝑝1 − 𝑝2)
Step 4: Table value of z at 𝛼 % level of significance
Step 5: If z ≤ z table value, H0 is Accepted
If z > z table value, H0 is Rejected
14. Z test
for
two proportions
Step 1: Null hypothesis H0: 𝑃1 = 𝑃2
Step 2: Alternative hypothesis H1: 𝑃1≠ 𝑃2 or 𝑃1 > 𝑃2 or 𝑃1 < 𝑃2
Step 3: Check Assumptions
Step 4: Test statistic – Chi-square and p value
Step 5: Conclusion
• If p ≤ Level of significance (∝), We Reject Null hypothesis
• If p > Level of significance (∝), We fail to Reject Null hypothesis
Assumptions Tests
𝑛1 × 𝑝1 > 10 and 𝑛1 × (1 − 𝑝1) > 10
𝑛2 × 𝑝2 > 10 and 𝑛2 × (1 − 𝑝2) > 10
____
15. Case Study
Two brands of coffee - Starbucks and CCD were to be compared. A sample of 100 under-
graduate students were selected and of them randomly 50 students were given Starbucks
coffee and remaining 50 were given CCD coffee. Coffee were served to them without brand
labels. 42 students liked the taste of Starbucks coffee while 45 students liked the taste of CCD
coffee. Is there a significant difference in likeness of the two brands for the under-graduate
students?
16. Null & Alternative
Hypothesis
Step 1: H0: 𝑃1 = 𝑃1
[There is no significant difference in likeness of the two brands]
Step 2: H1: 𝑃1 ≠ 𝑃1
[There is significant difference in likeness of the two brands]
(Two-tailed test)
17. Data in SPSS
50 students were given
Starbucks coffee and
remaining 50 were given
CCD coffee. Coffee were
served to them without
brand labels. 42 students
liked the taste of Starbucks
coffee while 45 students
liked the taste of CCD
coffee
22. Output
The Chi-square value is 0.796 and
p value = 0.372 > 0.05.
We fail to reject the Null hypothesis.
∴ There is no significant difference in likeness of the two
brands among under-graduate students
Z=
𝑝1 − 𝑝2
𝑃∗𝑄 (
1
𝑛1
+
1
𝑛2
)
=
0.84−0.90
0.87∗0.13 (
1
50
+
1
50
)
= 0.8955
Chi-Square = Square of z value
23. THANK YOU
Dr Parag Shah | M.Sc., M.Phil., Ph.D. ( Statistics)
pbshah@hlcollege.edu
www.paragstatistics.wordpress.com