as double mathematics - help · as double mathematics green block p1, ... (x, y) plane topic 3 ......

Name:________________________

AS Double Mathematics

Green Block

P1, P2, Stats+Mech Teacher:IngridFlynn

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Checklist for Completed Assignments:

o The assignment cover sheet has boxes ‘Done’ and ‘Ready’ ticked for every question, and none of these ticks are a lie

o Each question is started on a new side of A4 o Question numbers are written as a large title at the top of every page and underlined

twice: e.g. “Question 1 ”. o All questions are in order o Equals signs are all in a straight vertical line down the page (no snaking!) o All questions are written neatly and all working is shown o Mistakes are boxed off neatly and scored out o Answers are underlined twice and checked (show it has been checked by ticking it) o All pages are stapled together in the top left corner

Example:

Assignment Test

You will have an 30min assignment test on the day you hand in your assignment. There will be 5 questions which are identical to the questions in the assignment. Therefore, everyone should pass this test.

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Your Exams The Pearson Edexcel Level 3 Advanced GCE in Mathematics consists of three externally-examined papers:

Paper 1: Pure Mathematics 1 (*Paper code: 9MA0/01) Paper 2: Pure Mathematics 2 (*Paper code: 9MA0/02) Paper 3: Statistics and Mechanics (*Paper code: 9MA0/03) Each paper is: 2-hour written exam with calculator; 33.33% of the qualification; 100 marks. To get an E you need an average of about 45% in the exams. To get an A grade you need an average of roughly 85%.

PURE (Paper 1 and Paper 2) ● Topic 1 – Algebra and functions ● Topic 2 – Coordinate geometry in the (x, y) plane ● Topic 3 – Sequences and series ● Topic 4 – Trigonometry ● Topic 5 – Proof ● Topic 6 – Exponentials and logarithms ● Topic 7 – Differentiation ● Topic 8 – Integration ● Topic 9 – Numerical methods ● Topic 10 – Vectors STATISTICS (Paper 3, Section A) ● Topic 1 – Statistical sampling ● Topic 2 – Data presentation and interpretation ● Topic 3 – Probability ● Topic 4 – Statistical distributions ● Topic 5 – Statistical hypothesis testing MECHANICS (Paper 3, Section B) ● Topic 6 – Quantities and units in mechanics ● Topic 7 – Kinematics ● Topic 8 – Forces and Newton’s laws ● Topic 9 – Moments

Next Year’s Exams: Further Maths A Level (4 in total, each 1.5hr and 25%):

Compulsory: Core Pure 1, Core Pure 2 Options x2: Choose one from { FP1,FS1,FM1,D1} and {FP2,FS1,FM1,D1,FS2,FM2, FS1,D2}

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Your Teacher: Ingrid www.ingridflynn.weebly.com

Warning: I am very strict with homework so don’t even bother trying to get away with not doing all of the work I set (which is a lot)! I am also very helpful… I am (almost) always in room 3 or room 11 to give help if you need it.

Your Lessons

BRING THIS PACK TO EVERY LESSON PLEASE

In the first 3 half terms (about 19 weeks) we will study the course content, then for the next two half terms (about 12 weeks) we will practice the techniques, consolidate your learning and prepare for the exams.

Before each lesson you will have watched a video introducing a new topic. In total, this is usually about an hour’s work per week. In the lesson you will, for most of the time, be working rather than listening to me talk. You will be practicing basic mathematical skills and strengthening your understanding of the new topic by working through exercises, together with developing your problem solving skills by attempting to solve complicated problems using the maths you have learned.

Calculators

You need a calculator for this course. The recommended calculator is the

Casio Fx-991ex Classwiz (~£22).

Some doubles students choose to buy the Casio fx9860GII, an expensive but very good graphical calculator (around £70 from www.calculatorsdirect.co.uk) which is a huge advantage in the exams as it will solve all the equations for you, so you can check your answers. Slightly better (same functions but colour screen and nicer graph sketcher) is

the Casio fx-CG20 (around £100). Please talk to me if you are worried about buying a calculator.

Expectations. You will…

1. Attend all lessons and contact me as soon as possible if a lesson needs to be missed. You will check the Absence Box when you return to catch up on any missed work

2. Come to each lesson on time 3. Work hard in lessons 4. Hand in a complete, well presented assignment on last lesson of each week 5. Prepare fully for the weekly assignment test by practising 6. Ask for help if you need it, not wait for me to come to you and offer help 7. If an assignment test is not passed, you will need to re-do the incorrect questions twice each and

also find two similar questions to do (for each incorrect question). These will be handed in with the next assignment.

Assignments You will be set 1 assignment per week. It will always have the same format. You will have 9 hours of maths lessons per week, and are expected to do 9 hours of study out of lessons also in order to keep up with the pace of the course. Some of you will complete the assignment in 2 hours. Some of you will take 6 or 7 hours to complete it. It is your responsibility to make sure you start early enough to ensure you meet the deadline. Videos Eachweek,youwillbesetvideostowatchtointroduceyoutoanewtechnique.Asyouwatchthevideo,completetheassociatedpackpagesthentickitoff.Feelfreetogetahead!VideoscanbeaccessedusingtheQRcodesoronmywebsite.

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Wk Wk

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Videos Half Term 1 Mins Watch by Page

ü

0 11/9 Pure: Simultaneous Equations 20 8-9 Statistics: Sampling 48

1 18/9 Pure: Trigonometry: Radians measure and application 17 10-11 Stats: Measures of Location and Spread: Median and IQR of a list 9 49-50 Stats: Measures of Location and Spread: Mean and S.D of grouped data (by hand)

10 51-52

Stats: Measures of Location and Spread: Mean and S.D of grouped data (using a calculator)

3 53

Stats: Measures of Location and Spread: Mean and IQR of grouped data (Interpolation)

Stats: Measures of Location and Spread: Percentiles 7 55 2 25/9 Pure: Trigonometry: Mini Trig Equations 13 12-13

Pure: Trigonometry: Reciprocal Trig Functions 3 14 Pure: Trigonometry: Reciprocal Trig Graphs 13 15 Pure: Trigonometry: Pythagorean Trig Identities - Proof 6 16 Pure: Trigonometry: Using Trig Identities to Solve Equations 2 17 Stats: Linear Coding 6 56 Stats: Combined mean 2 57

3 2/10 Pure: Arithmetic Series and Proof 25 L1 18-20 Pure: Geometric Series and Proof 17 L3 21-23 Stats: Histograms: Intro 3 L2 58 Stats: Histograms: Dimensions of Bars 6 L2 59

4 9/10 Pure: Binomial Expansion: Finite 24-26 Pure: Recurrence Relation 6 L2 27 Pure: Sigma Notation 22 L2 28 Stats: Probability: Venn Diagrams: Union 5 L3 60 Stats: Probability: Venn Diagrams: Intersection 5 L3 61 Stats: Venn Diagrams: Addition Rule 8 L3 62

5 16/10 Pure: Factor Theorem Pure: Algebraic Division 4 L2 29 Stats: Probability: Venn Diagrams: Given (Conditional Probability) 10 L3 63 Stats: Probability: Tree Diagrams 6 L3 64 Stats: Probability: Tree Diagrams: Given (Conditional Probability) 6 L3 65

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6 30/10 Pure: Algebraic Fractions 4 L1 30 Pure: Partial Fractions 16 L3 31-32

7 6/11 Pure: Proof by Contradiction and Deduction 13 L1 33-34 Pure: Proof by Exhaustion 9 L1 35 Stats: Probability: Mutually Exclusive and Independent Event 5 L2 66

Stats: Statistical Distributions – DRVs 7 L3 67 Stats: Statistical Distributions – Discrete uniform distribution 3 L3 68

9 20/11 Pure: Trigonometry – Compound Angle Formulae 9 L1 36 Pure: Trigonometry – Double Angle Formulae 3 L1 37 Stats: Statistical Distributions – Binomial Distribution 10 L3 69

10 17/11 Stats: Hypothesis Testing – Binomial Distribution 10 L2 70 Stats: Hypothesis Testing – Lower Tails Test 9 L3 71 Stats: Hypothesis Testing – Upper Tails Test 7 L3 72

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11 4/12 Pure: Exponentials and Logs – The Basics 14 L1 38-39 Pure: Exponentials and Logs – Sketching e^x and lnx 6 L1 40-41

Pure: Exponentials and Logs – Solving Equations 8 L2 42-44 Pure: Exponentials and Logs – Modelling 5 L2 45

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Wk Wk begins Videos Half Term 3 Mins Watch

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13 1/1 Stats: Hypothesis Testing – Critical Values - Lower Tail Test 8 73 Stats: Hypothesis Testing – Critical Values - Upper Tail Test 8 74 Stats: Hypothesis Testing – Critical Regions - Two Tail Test 16 75

14 8/1

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Pure

● Topic 1 – Algebra and functions ● Topic 2 – Coordinate geometry in the (x, y) plane ● Topic 3 – Sequences and series ● Topic 4 – Trigonometry ● Topic 5 – Proof ● Topic 6 – Exponentials and logarithms ● Topic 7 – Differentiation ● Topic 8 – Integration ● Topic 9 – Numerical methods ● Topic 10 – Vectors

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Pure - Simultaneous Equations Linear and quadratic simultaneous equations Equations and inequalities 20 min

Write down the easier equation Rearrange into y = or x = Sub that the harder equation Solve to find y (or x) Use the easy equation to find x (or y)

Level 1 2041032

=+

=+

yxyx

Little sketch of what you’re finding:

Level 2 2041032

2 =+

=+

yx

yx Little sketch of what you’re finding:

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Write down the easier equation Rearrange into y = or x = Sub that the harder equation Solve to find y (or x) Use the easy equation to find x (or y)

Level 3 2041032

22 =+

=+

yx

yx Little sketch of what you’re finding:

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Pure - Trigonometry Radian measure and its applications (TOOLS) 17 min

T Triangle Area

O Sector Area O Arc Length

L Cosine Rule

S Sine Rule

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Pure - Trigonometry Graphs of standard trig functions 13 min and solving mini trig equations

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sin =x 3600 ≤≤ x

23

sin =x π20 ≤≤ x

13

23

cos −=x 3600 ≤≤ x

2 tan x = - 2 3600 ≤≤ x

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Pure - Trigonometry Reciprocal trig functions 3 min

Write down the three reciprocal trig functions

Secant ! (Sec !) =

Cosecant ! (Cosec !) =

Cotangent (Cot !) =

Work out the value of this function:

Sec 60° =

Top Tip for remembering which is which:

Circle the first letter: sin x cos x tan x

Circle the third letter: cosec x sec x cot x

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Pure - Trigonometry Reciprocal trig graphs 13 min

y = cosec !

y = sec !

y = cot !

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Pure - Trigonometry Pythagorean trig identities – proof 6 min

Prove that:1+cot2!=cosec2 !

Divide through by sin2 !

Prove that:tan2!+1=sec2!

Divide through by cos2 !

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Pure - Trigonometry Using Pythagorean Trig Identities to Solve Equations 2 min

This is an example of using a pythagorean trig identity to solve an equation.

Solve 4!"#$!!! − 9 = !"#$ !"# 0 ≤ ! ≤ 360

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Pure - Arithmetic Series 25 min

What do all these terms add up to?

Proof of the sum of an Arithmetic Series (to learn)

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Translate the information into maths using the two equations!

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Translate the following information

1 The 5th term is 11 2 The 8th term is 7 3 The sum of the first 8 terms is 12 4 The sum of the first 18 terms is -2 5 The 12th term is -17 6 The sum of the first 9 terms is 15 7 The 17th term is 91 8 The sum of the first 52 terms is 500 9 The 11th term is 9 10 The sum of the first 6 terms is -20

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Pure - Geometric Series and Proof 17 min

2,4,8,16,…,256,…,3276 What do all these terms add up to?

Proof of the sum of a Geometric Series (to learn)

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Translate the information into maths using the two equations!

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Translate the following information

1 The 5th term is 11 2 The 8th term is 7 3 The sum of the first 8 terms is 12 4 The sum of infinite terms is -2 5 The 12th term is -17 6 The sum of the first 9 terms is 15 7 The 17th term is 91 8 The sum of infinite terms is 500 9 The 11th term is 9 10 The sum of the first 6 terms is -20

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Pure: Binomial Expansion

( )

( )

( )

( )

( )

( )7

4

3

2

1

0

ba

ba

ba

ba

ba

ba

+

+

+

+

+

+

Finding the coefficients

Method 1:

Method 2:

Method 3:

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( )432 x+

( )71 x−

4

22 ⎟

⎠

⎞⎜⎝

⎛ −x

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( )42 px+

( )nx21+

Why is 0! = 1? Where does the rnC formula come from?! Why is it called n ‘choose’ r? Watch these

videos to find out!

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Pure: Recurrence Relations This is an example of how to interpret 6 min recurrence relation notation

4,5 11 =+=+ uuu nn

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Pure: Sigma Notation 22 min

I haven’t left you much room here sorry – you need to make notes on what the notation is telling you to do and how you would answer the problem but don’t attempt to copy out everything from the screen! Just the key points to enable you to answer one of these questions.

( )∑=

−6

212

kk

( )∑=

+142

1027

rr

∑=

4

2

2r

r

∑=

10

4

3k

ku

4,5 11 =+=+ uuu nn

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Pure: Algebraic Division 4 min

Copytheexample !!!!!!!!!!!!"!!!!!!!

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Pure: Algebraic Fractions 4 min

Copy the two examples:

1) Simplify!!!!!!!!!!!

!!

2) Simplify!!!!!!!!!" ÷ !!!!!"

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Pure: Partial Fractions https://youtu.be/OeUCqui7bu0 16 min

Write !!!!!!! !!! inpartialfractions.Showthefullmethod

Write!!!!!!"! !!

!!! ! !!!! inpartialfractions.Showthefullmethod

….continuedonnextpage

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Pure - Partial Fractions Page 2

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Pure - Algebraic Methods - Proof Contradiction (Counter-example) 8 min

Definition of proof by contradiction:

Write down the proof that 2 is irrational

If !! is even then ! is even. Why is this true?

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Pure - Algebraic Methods - Proof Deduction 5 min

Definition of the proof by deduction:

Write down the proof that the sum of any two consecutive odd numbers is a multiple of 4:

Write down the useful definitions of:

Even numbers

Odd numbers

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Pure - Algebraic Methods - Proof Exhaustion 9 min

Definition of the proof by exhaustion:

Write the proof of the conjecture that 97 is a prime number:

As there are no factors < 97 ………

(Make sure you conclude your proof)

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Pure: Trigonometry - Compound Angle Formulae https://youtu.be/DyqQG7MzOPU 9 min

sin(A±B)=sinAcosB±cosAsinB

cos(A±B)=cosAcosB∓sinAsinB

tan(A±B)= !"#!±!"#! ! ∓!"#$ !"#$

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Pure: Trigonometry - The Double Angle Formulae https://youtu.be/upkil94kk_g 3 min

sin2A=2sinAcosA

tan2A= ! !"#!!!!"#! !

cos2A=cos! ! − sin! !

Therearetwootherformulaeforcos2A.

cos2A=2 cos! ! − 1

cos2A=1 − 2 sin! !

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Pure - Exponentials and logs The basics 14 min

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1. 2log3 =x 2. 416log =x 3. 2log4=x

4.21

log9 =x 5.31

2log −=x 6. x3log3 =

7. 2log31

x= 8.21

log16 −=x 9. x=25log5

10. x4log21=−

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Pure - Exponentials and logs Sketching !! and !"# 6 min

y = ex Check on your calculator!

y = e2x y = ex+1 y = e-x

y = ex+1 y = 2ex y =- ex

Remember to show the x-intercept and/or y-intercept

Always label the equation of the asymptote!

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y = lnx Check on your calculator!

y = ln(x+1) y = ln(-x) y = ln(2x)

y = lnx+1 y=-lnx

Remember to show the x-intercept and/or y-intercept

Always label the equation of the asymptote!

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Pure - Exponentials and logs Solving equations using logs and powers 8 min

Useful Facts: Formula 1: Formula 2: Formula 3: Formula 4: 1. 4log2 =x 2. 185 =x 3. 024log8log4 =−− xx 4. 56772 =+ xx

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5. 3loglog 39 =+ xx 6. 03339 1 =+−− + xxx

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7. ( ) 24loglog2 33 =+− xx

8. ⎟⎠

⎞⎜⎝

⎛−+41

log6log5log 101010

9. ( ) ( ) 02196log32log2 2

33 =+−−− xxx Answers

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Pure - Exponentials and Logs Modelling using logarithmic and power relationships 5 min

Sarah Swift got a speeding ticket on her way home from work. If she pays the fine now, there will be no added penalty. If she delays her payment, then a penalty will be assessed for the number of months, that she delays paying her fine. Her total fine, f in Euros is indicated in the table below. These numbers represent an exponential function.

Number of months t payment is delayed

Amount F of the fine

1 300

2 450

3 675

4 1012.50

What is the common ratio of consecutive values of F?

Write the formula for this function F =

What is the fine in Euros for Sarah’s speeding ticket if she pays it on time?

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Statistics

(Paper 3, Section A) ● Topic 1 – Statistical sampling ● Topic 2 – Data presentation and interpretation ● Topic 3 – Probability ● Topic 4 – Statistical distributions ● Topic 5 – Statistical hypothesis testing

48

Statistical Sampling

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Statistics - Measures of location and spread Median and Interquartile Range (IQR) 9 min

2|5means25

0 6 7 8 1 0 2 3 4 7 7 7 8 9 2 1 3 4 5 5 7 3 1 1 2 6 6 9 4 1 5 5 6 9 5 6 7 9 Findthelowerquartile,median,upperquartile,IQRanddecideifthereareoutliers.

Ifitisawholenumber…………………………………………………………………….

Ifitisnotawholenumber…………………………………………………………………

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Keystem=10s

9 0 6 8 3 5 7 7 1 6 6 6 0 2 2 4 5 1 1 2 4 3 4 7 8 3 5 7 2 1 6 Findthelowerquartile,median,upperquartile,IQRanddecideifthereareoutliers

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Statistics - Measures of location and spread Mean and S.D with grouped data 10 min

Ungroupedfrequency

Maths test mark

No of people

1 6 2 5 3 7 4 4

Findthemeanandstandarddeviation

Groupedfrequency

height frequency 0-4 2 5-10 4 11-16 6 17-20 5 21-30 5

Findthemeanandstandarddeviation

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Ungroupedfrequency

No of pets owned

No of people

1 4 2 6 3 2 4 2 Findthemeanandstandarddeviation

Groupedfrequency

English mark

Frequency

5-14 3 15-19 4 20-29 5 30-34 2

Calculatethemeanandstandarddeviation

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Statistics - Measures of location and spread Mean and S.D of grouped data (by calculator) 3 min

x f

1 7

2 10

3 13

4 9

5 4

The buttons I need to press to calculate the mean and sd are:

54

Statistics - Measures of location and spread Interpolation Median and Interquartile Range (IQR) of grouped data

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Statistics - Measures of location and spread Percentiles 7 min

Example 1 Calculate the 50th percentile for Bethany

43,54,56,61,62,66,68,69,69, 70,71,72,77,78,79,

85,87,88,89,93,95,96,98,99,99

Example 2 Calculate the 40th percentile for DeKwanye East

43,54,56,61,62,66,68,69,69, 70,71,72,77,78,79,

85,87,88,89,93,95,96,98,99,99

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Statistics - Measures of location and spread Linear Coding 6 min

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Statistics - Measures of location and spread Combined mean 2 min

Nadir asked 15 students about their AP results, their mean was 62.

He later asked 25 students about their AP results, their mean was 71.

Work out their combined mean.

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Statistics – Histograms Intro This video shows you the key features of Histograms 3 min

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Statistics – Histograms - Dimensions of Bars This video shows you how to find the dimensions of a Histogram 6 min

IMPORTANT!!!

CHECK THE BAR WIDTH!

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Statistics: Probability: Venn Diagrams: Union

P(A∪B) 5 min Watch the examples then complete the questions for the Venn diagram shown (showing all working!) What is the tick rule for union?

i) P(A∪B)

ii) P(A∪B’) =

iii) P(A’∪B) =

iv) P(A’∪B’) =

v) P(B∪B’) =

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Statistics: Probability: Venn Diagrams: Intersection

P(A∩B) 5 min

What is the tick rule for intersection?

i) P(A∩B) =

ii) P(A∩B’) =

iii) P(A’∩B) =

iv) P(A’∩B’) =

v) P(B∩B’) =

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Statistics: Probability: Venn Diagrams: Addition Rule Venn diagrams 8 min

Venn Diagrams

Formulae to Learn:

Addition Rule

Mutually Exclusive:

Independent:

!(!′ ∪ !⬚ )∪

P(AUB)’

OR=

AND=

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Statistics: Probability: Tree Diagrams Tree diagrams 6 min

Abagcontains3blueballsand5redballs.Twoareselectedatrandomwithoutreplacement.Findtheprobabilitythat

a)theyarebothblue

b)thereisoneofeachcolour

Pythagoras tree…look it up!

Thereare5blacksocksand3redsinabag.Ipick2sockswithoutreplacement.FindtheprobabilityIget

a)twoofthesamecolouredsock

b)atleastoneredsock

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Statistics: Probability: Tree Diagrams: Given Interpreting conditional probability using tree diagrams 6 min

66

Statistics - Probability Mutually exclusive and independent events 5 min

67

Statistics - Statistical distributions Discrete Random Variables (DRVs) 7mins

FindtheprobabilitydistributionforSthescoreonadie.

AdieisthrownuntileitherasixappearsorI’vethrownitthreetimes.FindtheprobabilitydistributionforTwhereTisthenumberofthrows.

68

Statistics - Statistical distributions Discrete uniform distribution 3mins

Write down the rules you need to learn:

69

Statistics - Statistical distributions Binomial Distribution 10mins

Write down the four properties for a binomial distribution:

i)

ii)

iii)

iv)

Example,

A die is thrown three times and a success is defined as when a 6 is thrown:

70

Statistics - Hypothesis testing for Binomial Test for a Binomial distribution 10 min

A 6 sided die is thrown 30 times and the number of sixes recorded.

Let X be the r.v. number of6’s thrown in 30 throws, !~ !(30, !)

0 1 2 3 4 5 6 7 8 9 10 …

One Tail Tests

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Statistics - Hypothesis testing Lower tails test 9 min

Is a normal six sided die fair when 1 six is thrown in 24 throws?

Let X be the r.v. number of6’s thrown in 24 throws, !~ !(24, !)

On the Casio fx-991EX

To find the probability that x = 1 in the above example, follow these instructions

Menu

7: Distribution

4: Binomial

2: Variable

X: 1

N: 24

P: 1 ÷ 6 get p = 0.06037975302

Can then find the probability x = 0 and add them.

(0.06037975302 + 0.01257911521 = 0.07295886823)

Alternatively, to find a cumulative probability x ≤ 1, which can be more useful in general, follow these.

Menu

7: Distribution

Scroll down to 1: Binomial CD

2: Variable

X: 1

N: 24

get 0.07295886823, as before

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Statistics - Hypothesis testing Upper tail tests 7 min

In Luigi’s restaurant on average 1 in 10 people order a bottle of Chardonnay. Out if a sample of 50 people, 11 chose Chardonnay. Has the drink become more popular? Test at the 1% level of significance.

Let X be the r.v.’ number people ordering a bottle of Chardonnay out of a sample of 50, where !~ !(50 !)

Conclusion

Please note

Where he refers to tables, use Casio fx-991EX instead.

Adapting instructions for Binomial CD from before to find p(X ≤ 10),

X: 1

N: 50

P: 0.1 get 0.9906453984

Then required probability is 1 - 0.9906453984 = 0.0093546…

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Statistics - Hypothesis testing Critical values – lower tail test 8 min

A manufacturer claims that 2 out of 5 people prefer Soapy Suds washing powder over any other brand. For a sample of 25 people only 4 people are found to prefer Soapy Suds. Is the manufacturers claim justified? Test at the 5% level of significance.

Conclusion

Please note


Adapting instructions for Binomial CD from before to find p(X ≤ x),

X: try x = 2, 3, 4 … until you reach a probability greater than 5% (0.05)

N: 25

P: 0.4

This occurs when p(x ≤ 6) = 0.0735…, so X = 5 is the critical , p(x ≤ 5) = 0.0294

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Statistics - Hypothesis testing Critical regions – upper tail test 8 min

A particular drug has a 1 in 4 chance of curing a certain disease. A new drug is developed to cure the disease. How many people would need to be cured in a sample of 20 if the new drug was deemed more successful at curing the disease than the old drug to obtain a significant result at the 5% level?

Let x be the r.v. ‘Number of people cured by the new drug’, where !~ !(20 !)

Conclusion

Please note


Adapting instructions for Binomial CD from before to find p(X ≤ r – 1) ≥ 0.95

X: try x = 6, 7, 8, … until you reach a probability greater than 0.95

N: 20

P: 0.25

So r – 1 ≥ 8, r ≥ 9

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Statistics - Hypothesis testing Critical regions – two tail test 16 min A person suggests that the proportion, p of red cars on a road is 0.3. In a random sample of 15 cars it is desired to test the null hypothesis against the alternative hypotheses p ≠0.3 of a nominal significance level of 10%. Determine the appropriate rejection region and the corresponding actual significance level.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Let X be the r.v. ‘Number of red cars in a sample of 15’, where !~ !(15 !)

Conclusion

Please note


Adapting instructions for Binomial CD from before to find

a) For lower tail p(X ≤ xL) ≥ 0.05

X: try x = 0, 1, … until you reach a probability greater than 0.05

N: 15

P: 0.3

xL = 1

b) For upper tail p(X ≤ xM- 1) ≥ 0.95

c) XM-1 = 7, XM = 8

as double mathematics - help · as double mathematics green block p1, ... (x, y) plane topic 3 ......

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