A Detailed Lesson Plan in Statistics and Probabilit1
September 18, 2022 | Author: Anonymous | Category: N/A
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A DETAILED LESSON PLAN IN STATISTICS AND PROBABILITY I. OBJECTIVES At the end of the lesson, the students should be able to: A. Utilize and interpret Pearson’s Correlation coefficient B. Calculate the coefficient using the formula and statistical tool/s C. Draw conclusion based on the Pearson’s Correlation Coefficient II. SUBJECT MATTER: “Pearson Product Moment (r) correlation coefficient” A. Reference: 1. Statistics S tatistics and Probability 2. Elementary Statistics B. Skills: Computing and Analyzing III. MATERIALS: Books, Computer, Calculator, PPT, Pentel Pen, Cartolina IV. PROCEDURE A. Developmental Method Method
Teacher’s Activity A. Preparation a. Review Class yesterday we discussed about hypothesis testing, right? So, let me ask you this question: “What is the difference between a Null and Alternative Hypothesis?”
Okay, Very Good.
Student’s Activity
Yes, Ma’am The null hypothesis suggests that there is no significant difference or relationship between the compared entities while Alternative hypothesis is the negation of the null hypothesis. It simply suggests that there is a significant difference or relationship between the compared entities.
What else?
Null hypothesis is denoted by H o while Alternative Hypothesis is denoted by H1
How about the construction of the null and alternative hypothesis?
The null and alternative hypotheses are constructed in a way that when we reject the null hypothesis, there is no other possibility other than to accept the alternative hypothesis. With this, the hypothesis proposed by researchers which is usually in favor of the alternative hypothesis has been supported.
Lastly, how about the 4 basic steps in testing a hypothesis?
1. State the hypotheses 2. formulate an analysis plan 3. Analyze sample data: Alpha level, p- value, Computed value and tabular value 4. Interpret Results
With that being said, is there any question about hypothesis testing? If none, kindly answer this example before we proceed to our today’s lesson? Example: A random sample of 100 suspected leptospirosis patients in Pangasinan last year shows that the symptoms exhibit within 72 hours. Does the project that the symptoms would exhibit earlier than the common 80 hours with a standard deviation of 16 hours?
Test t he he hypothesis at α= 0.05 level of significance. What are the hypotheses?
H0: μ= 80 hours H1: μ< 80 hours
= 7280 16 1 100 00 √ = |5| 5 |
How about the z computed value? Kindly show your solution on the board?
Kindly recite your decision?
Very Good Class, Any question about hypothesis testing? b. Motivation Okay class, let have first a short activity before our lesson.
Decision: Since the absolute value of the computed z- value = 5 is greater than the absolute value of the critical value of z= 1.64 then we reject the null hypothesis and accept the alternative hypothesis. This means that the symptoms of leptospirosis exhibits in less than 80 hours.
None Ma’am. Yes Ma’am.
Let the students play with JUMBLED WORDS. The students are group into 4, the group who correctly arranged the jumbled words, First will get 1 point. The jumbled words will be handed over to students. The students will post their answer on the board. The winner of the game will receive a token. JUMBLED WORDS 1. ELCXE 2. ORATLCUACL 3. EUMCOPTR
The students response must be the following: 1. EXCEL 2. CALCULATOR 3. COMPUTER 4. HYPOTHESIS 5. CORRELATION
4. YPHSSHPTEI 5. ORLTOCREAIN Do you know that those words will help you with our lesson today?
No Ma’am
Those words that you see on the board will enlighten you in our lesson for today. Some words will help you and some will guide you through the process. B. Presentation So be with me this morning class, as I discuss to you about “Pearson Product Moment (r) of correlation coeff icient.” icient.” Everybody Read! a. Statement of the aim
“Pearson Product Moment (r) of correlation coefficient.”
Class listen carefully because after my discussion you will be asked to compute, interpret a problem using Pearson r correlation and lastly, you will be ask to draw a conclusion from a given set of problem.
Yes Ma’am.
Am I understood Class? C. Developmental Proper Class, are you familiar with Aristotle? Newton? Pythagoras?
Yes, Ma’am. Yes, Ma’am. Yes, Ma’am.
How about Karl Pearson? Let me introduce to you Sir Karl Pearson.
NO ma’am
He developed a rigorous mathematical treatment to describe the relationship between two variables now known as the PEARSON PRODUCT- MOMENT Coefficient Correlation.
Okay Ma’am.
With that being said, what are you trying to describe using Pearson Correlation?
Using Pearson Correlation, we can describe the relationship of variables.
How many variables?
Two variables ma’am.
Okay class so there are four concerns raised when doing a regression analysis. There are four concerns raised when doing regression analysis. 1. Relationship of the variables 2. Strength of the relationship 3. Type of relationship 4. Predictions that can be made from the relationship
There are four concerns raised when doing regression analysis. 1. Relationship of the variables 2. Strength of the relationship 3. Type of relationship 4. Predictions that can be made from the relationship
Kindly Read!
Here’s the formula in finding the r - value. Linear correlation coefficient is used to determine the strength of a linear relationship between two variables. It is denoted by the variable and is computed using the following formula:
= [ (∑ )∑∑ ] [[∑∑(∑∑) ∑ ]
where n is the number of data pairs, x is is the first set of variable and y is is the second set of variable. Are you familiar with PEMDAS?
Yes Ma’am. P- parenthesis E- Exponent M- Multiplication D- Division A- Addition S- Subtraction
Very Good! You have to follow PEMDAS in order for you to get the correct answer for rvalue.
No Ma’am. Why ma’am? Don’t you know class that it is important to note that an r- value is meaningless if not interpreted? Because in statistics, for every numerical value obtained, there is an equivalent descriptive interpretation. interpretation. The value of Pearson r Correlation can be interpreted as follows:
Yes Ma’am.
Am I understood, Class? Okay, Let’s have this example. Example: The scores of ten randomly selected senior high school student on the mathematical portion of the National Achievement Test (NAT) and mathematical ability part of a university admission test were recorded as follows: Scores on Scores on NAT Admission Test (y) Student No. (x) 1 5 6 2 7 15 3 9 16 4 10 12 5 11 21 6 12 22 7 15 8 8 17 26 9 20 5 10
26
30
The teacher will check their answer.
xy
y
5
6
25
7
15
49
225
105
9 10
16 12
81 100
256 144
144 120
11
21
121
441
231
12
22
144
484
264
15
8
225
64
120
17
26
289
676
442
20
5
400
25
100
26
30
676
900
780
10
51
36
∑ = ∑ = 13
The student will show his/her solution on the board.
x
2
36
∑ = 21
16
1
30
∑ = 32
∑ =
23
Substitute every value to the formula of the coefficient of correlation
= [ (∑ )∑∑ ] [[∑(∑∑) ∑ ] 10102336 161 2336 132 132 161 = 10 13210103251 3251 161 10 2110 2110 2108 = = 0.428 36766589 36766589
What is your interpretation from the obtained r- value?
The r value of 0.428 indicates a substantial relationship. Since r is is positive, it means that a
senior high school student who will get a high score on the mathematical portion on the National Admission Test (NAT) will also score high on the mathematical ability part of a university admission. Likewise, if the student will get a low score on the NAT, he will also have a low score on the mathematical ability part of a university admission.
Very Good, Class!
That’s how you get the r-value. Moreover, we introduced PPMCC or simply r as a measure of the STRENGTH of a relationship between two variables x and y. But any relationship should be assessed for its SIGNIFICANCE as well as its STRENGTH.
It’s Long and time consuming ma’am!
So in testing the SIGNIFICANCE of r, we need to follow the procedure. 1. State the Null and Alternative Hypothesis 2. Set the level of significance and Degree of freedom wherein df= n-2 3. Employ a two-tailed test and degree of freedom. Locate the tabular value of t.
1. State the Null and Alternative Hypothesis 2. Set the level of significance and Degree of freedom wherein df= n-2 3. Employ a two-tailed test and degree of freedom. Locate the tabular value of t. 4. Compute for the value of the t- statistics:
4. Compute for the value of the tstatistics:
= 122
= 1 22
5. State the Decision
5. State the Decision. Note: Decision Rule- Reject Ho If t comp comp ≥ t ttab ab. What is the decision rule in testing the significance of r?
Decision Rule- Reject Ho If t comp comp ≥ t tab tab.
Am I understood Class?
Yes Ma’am.
Then, Let us test the significance of r from example no. 1 following the procedure given. What would be the hypothesis? 1. Ho= There is no significant relationship between students’ score in math NAT and score in Math Admission Test
Very Good, How about the level of significance and df?
H1= There is significant relationship between students’ score in math NAT and score in Math Admission Test
2. α= 0.05 df= 8 What is the tabular value? What is the value of t- statistic? Show your solution.
3. t tab= 2.306 4.
= .428 −− −.
= .428 10. 8183 = .428 .8 817 =.428√ 28 =√ 9.91..739239
Very Good! And Lastly, State your decision.
5. Decision: Since the t comp comp= 1.339 < t tab tab= 2.306. I therefore accept the Null hypothesis and reject the Alternative Hypothesis. It means that the students’ score in math on NAT and Admission Test is not significantly related.
How do you feel while solving the Pearson R Correlation?
Enjoyed it but its time consuming because of the process of solving it.
Really? Okay Class, let me introduce to you a statistical tool that you may use in this lesson at the same time in your research. Are you guys excited? Have you heard of the word Excel?
Yes Ma’am.
Yes Ma’am
Bring out your laptop and follow the instruction in installing Data Analysis. 1. 2. 3. 4. 5. 6.
Open Excel Click File Click options Click Add Ins Click Analysis ToolPak then GO Check Data Analysis ToolPAk and VBA 7. Then Data, check if Data Analysis was successfully installed. Can you follow the procedure? You can use this in computing for the r and significance of r. To appreciate this toolpak, we will be using the same example 1. Just Simply Type the values of x and y.
Then Click data analysis, look for regression.
Input: Variable X and Y. Highlight the values of Y and X, respectively
Yes Ma’am
Click Output Range, Make sure to click it anywhere in the sheet. You will see this.
See, the value of the multiple R there is the rvalue and the t- stat in the X variable 1 will be the t computed value. Is it easy? What can you say about data analysis? Yes, but take note class that you will just use Data analysis in your activity and future calculations but you are not allow to use this in your exam. IS that clear? Any question about Pearson Product Moment Correlation Coefficient?
Okay, Let’s proceed to your activity!
Yes, Ma’am!
It’s easy to follow and not time consuming.
Yes Ma’am! None Maam.
D. Application Students are grouped into four. Each group will be given problem set. Cartolina/ Manila Paper and Pentel Pen. Each student should participate in this activity. Teacher will assign a leader. Leader will assign her member. Someone will compute, interpret and explain the results in front of the class. ACTIVITY Direction: Use Excel in Computing for r- value and its significance. Follow the steps in showing your answer. 1. The age and systolic blood pressure (SBP) readings of 15 individuals were recorded as follows: AGE SBP 32 115 35 123 36 125 40 100 43 120 44 120 46 131 48 130
1. Ho= there is no significant relationship between the age and systolic blood pressure H1= there is a significant relationship between the age and systolic blood pressure 2. α= 0.05 df= 15-2= 13 3. ttab= 2.160
50 140 53 152 60 133 61 148 64 155 71 163 75 165 a. Compute Pearson r and interpret its value
b. Is there athe significant between age and relationship systolic blood pressure? Use α= 0.05
2. A study was made to determine the relationship between monthly advertising expenditures and sales. The following data were recorded: Advertising Cost Sale (in Thousands) (in thousands) 8 77 4 80 5 79 4 73 6 95 10 88 8 98 4 84 10 112 8 105 5 96 10 102 a. Calculate Pearson r and interpret its value b. Test the significance of r at 0.05 level
4. 5. Since the t computed= 6.633 greater than (>) t tab= 2.160, reject the Ho, accept H1. Therefore, there is significant relationship between the age and systolic blood pressure.
1. Ho= There is no significant relationship between monthly advertising expenditures and sales. H1= There is a significant relationship between monthly advertising expenditures and sales 2. α= 0.05 df= 12-2= 10 3. t tab= 2.228 4.
5.
Decision: Since the t computed= 2.598 greater than (>) t tab= 2.228, reject the Ho, accept H1. Therefore, there is significant relationship between the monthly advertising expenditures and sales.
V. Evaluation Direction: Bring out your big note book and answer the problem, manually, using the formula. 1. The test score in Mathematics and Science of 12 college students are recorded as follows: Student Math Science No. Scores Scores 1 18 20 2 16 18 3 11 12 4 5 6
15 15 11
17 15 14
1. Ho= there is no significant relationship between score in mathematics and science H1= there is a significant relationship between score in mathematics and science
7 8 9 10 11 12
11 13 8 9 13 7
12 14 10 13 12 9
a. Compute the Pearson r at 0.05 level of significance b. Is there a relationship between score in mathematics and science? VI. Assignment 1. What is Spearman Rank- Order Coefficient of Correlation (rs) 2. Formula for Spearman rho 3. How to test the significance or r s? PREPARED BY:
ABBYGAIL D. BALGUA MED- MATH ED.
SUBMITTED TO:
MICHAEL HOWARD MORADA PROFESSOR
2. 3. 4. 5.
α=0.05 r= 0.92 t tab= 2.228 df= 10 t comp= 7.42 Since t comp is greater than t tab, i.e, 7.42> 2.228, therefore reject Ho. A students’ score in mathematics is significantly related to his score in science.
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