Скачать или смотреть Probability Distributions & Hypothesis Testing (Q3 AS Statistics Edexcel 2025)

In this AS Statistics walkthrough, Lee Guffick (former Head of Maths & A-Level Examiner) tackles Question 3 (Edexcel 2025): modelling coloured counters with a Binomial distribution and running a one-tailed hypothesis test at 5% significance. You’ll see why with replacement ⇒ Binomial, how to state
𝐻
0
H
0
​

and
𝐻
1
H
1
​

correctly, compute a p-value (≈ 0.161 for
𝑋
greater than or equal to
11
X greater than or equal to 11 when
𝑛
=
40
,
 
𝑝
=
0.2
n=40,p=0.2), and identify the acceptance region (
𝑋
less than or equal to
12
X less than or equal to
12) vs the critical region (
𝑋
greater than or equal to
13
X greater than or equal to13). Clear, exam-ready, and aligned to how Edexcel marks.

⏱️ TIMESTAMPS
00:00 Intro & question set-up
00:36 Proportions → finding
𝑝
p for “red”
01:25 Why Binomial? (4 conditions: fixed
𝑛
n, constant
𝑝
p, independence, two outcomes)
02:35 Defining the distribution for red counters
03:30 Hypothesis test for green counters (one-tailed,
5
%
5%)
04:28 Choosing PD vs CD on calculator & tail logic
05:20 Calculating p-value for
𝑋
≥
11
X≥11
06:10 Compare with 0.05 → decision wording (“insufficient evidence to reject
𝐻
0
H
0
​

”)
07:05 Acceptance region vs critical region (why
𝑋
less than or equal to
12
X less than or equal to12,
𝑋
greater than or equal to
13
X greater than or equal to13)
08:10 Examiner tips & common pitfalls

✏️ TOPICS COVERED

Binomial model: conditions, parameters, and notation

Calculator strategy: Binomial PD/CD and right-tail probabilities

Hypothesis testing (one-tailed,
5
%
5% level):
𝐻
0
H
0
​

,
𝐻
1
H
1
​

, test statistic, p-value

Acceptance vs critical regions (discrete case,
𝑛
=
40
,
 
𝑝
=
0.2
n=40,p=0.2)

Precise exam language that earns marks

💯 EXAM TIPS

Always justify why Binomial (replacement ⇒ constant
𝑝
p, independence).

State
𝐻
0
:
𝑝
=
0.2
H
0
​

:p=0.2 and
𝐻
1
:
𝑝
greater than
0.2
H
1
​

:p greater than 0.2 clearly for a one-tailed test.

Quote the p-value and compare to 0.05 before concluding (avoid saying “accept
𝐻
0
H
0
​

”; write “insufficient evidence to reject
𝐻
0
H
0
​

”).

For discrete tests, specify acceptance/critical regions using integer cut-offs.

📚 ABOUT GUFFICK TUITION
I’m Lee Guffick, former Head of Mathematics and A-Level Examiner. I help ambitious students secure A/A* and places at Oxbridge, G5, and top US universities with premium small-group programmes and targeted 1:1 support.

📅 JOIN OUR PROGRAMME
→ 1:1 Tutoring: https://www.gufficktuition.com/tutoring

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📱 CONNECT WITH LEE
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→ Email: [email protected]

Keywords: Edexcel AS Statistics 2025, Binomial distribution, hypothesis testing one-tailed, p-value, acceptance region, critical region, PD vs CD, A-Level Maths revision, Guffick Tuition

Hashtags:
#ALevelMaths #EdexcelMaths2025 #StatisticsRevision #BinomialDistribution #HypothesisTesting #MathsTutor #GuffickTuition