Detail Profil Mahasiswa

FRIZZY LITHMENTSYAH
Program Studi
Sains Data
Universitas
Institut Teknologi Sains Bandung (ITSB)
Mata Kuliah
Statistik Dasar
Dosen Pengampu
BAKTI SIREGAR, M.Sc., CDS.

1 CASE STUDY ONE: One-Sample Z-Test

CS 1

Digital Learning Platform Study Time

Hypotheses:
$H_0: \mu = 120$
$H_1: \mu \neq 120$ (Two-tailed)
Test Criteria:
$n = 64$ (Large sample)
$\sigma = 15$ (Known)

Calculations

Test Statistic (Z):

$$Z = \frac{\bar{x} - \mu_0}{\sigma / \sqrt{n}} = \frac{116 - 120}{15 / \sqrt{64}} = \frac{-4}{1.875} = -2.133$$

P-Value: $2 \times P(Z < -2.133) \approx \mathbf{0.033}$

Statistical Decision:
Since $P(0.033) < \alpha(0.05)$, we Reject $H_0$. The data suggests study time is significantly lower than claimed.

2 CASE STUDY TWO: One-Sample T-Test

CS 2

UX Research Task Completion

Justification: One-Sample T-test chosen because $\sigma$ is unknown and $n=10$ (small sample).
Mean ($\bar{x}$): 9.89
SD ($s$): 0.387
T-Stat: -0.899
P-Value: 0.392
Decision: $0.392 > 0.05$. Fail to Reject $H_0$. There is no significant evidence that completion time differs from 10 minutes.

3 CASE STUDY THREE: Independent Two-Sample T-Test

CS 3

A/B Test: Session Duration

Comparing Version A ($n=25, \bar{x}=4.8$) and Version B ($n=25, \bar{x}=5.4$).

Pooled SD ($s_p$) $\approx$ 1.304
T-Statistic $\approx$ 1.628
P-Value $\approx$ 0.110
Product Insight: Difference is not statistically significant. Avoid implementing Version B immediately; consider larger sample sizes to gain more power.

4 CASE STUDY FOUR: Chi-Square Test of Independence

CS 4

Device vs. Payment Preference

$\chi^2 = \sum \frac{(O-E)^2}{E} \approx 13.52$ | $df = 2$ | $P \approx 0.0012$
Statistical Decision: Reject $H_0$. Device and Payment method are associated.
Mobile: Prioritize E-Wallets.
Desktop: Highlight Credit Cards.

5 CASE STUDY FIVE: Error Analysis Framework

CS 5

Fraud Detection: Error Risk Assessment

Error Type Statistical Term Business Reality Primary Consequence
Type I $\alpha$ (False Positive) Rejecting a true $H_0$ (Thinking it works when it doesn't). Wasted resources & implementation costs.
Type II $\beta$ (False Negative) Failing to reject a false $H_0$ (Missing a working solution). Ongoing fraud losses & missed protection.
Business Criticality: Type II

In Fintech, Type II errors are often more catastrophic. A Type I error is a "sunk cost" (investment), but a Type II error represents "unbounded loss" as fraud continues to drain capital.

The Power of $n$

As sample size increases, the overlap between distributions decreases, reducing $\beta$ and increasing Statistical Power ($1-\beta$) without sacrificing $\alpha$.

Statistical Power Dynamics

Decreasing $\alpha$ (being stricter) naturally increases $\beta$ (missing more effects). To keep both risks low, the only "free lunch" in statistics is increasing the Sample Size, which sharpens the test's ability to detect the truth.

6 CASE STUDY SIX: P-Value & Model Evaluation

CS 6

Churn Model Performance Review

Test Statistic 2.31
p-value 0.021
Alpha ($\alpha$) 0.05
STATISTICAL DECISION

Since $P(0.021) \leq \alpha(0.05)$, we Reject the Null Hypothesis ($H_0$). The results are statistically significant at the 95% confidence level.

Executive Summary:

"Our analysis confirms the new churn model is effective. There is only a 2.1% probability that these results are due to random luck. We can confidently proceed with using this model to identify at-risk customers."

The Sampling Risk

If the sample isn't representative, we face Selection Bias. The model may look great on paper but fail in the real market, leading to wasted investment.

Significance vs. Size

A $p$-value detects existence, not impact. A "significant" model might only improve retention by 0.1%—statistically real, but practically negligible.

7 REFERENCES

07

Bibliography & Theoretical Foundations

Spiegelhalter, D. (2019). The Art of Statistics: How to Learn from Data. Basic Books.
Core Focus: A modern guide to understanding risk, uncertainty, and the nuances of statistical interpretation in daily life and business.

Wasserman, L. (2004). All of Statistics: A Concise Course in Statistical Inference. Springer.
Core Focus: Bridges the gap between classical frequentist inference and modern Machine Learning applications.

Casella, G., & Berger, R. L. (2002). Statistical Inference. Duxbury Resource Center.
Core Focus: The rigorous mathematical standard for graduate-level statistical theory and formal hypothesis testing frameworks.

"Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write." — H.G. Wells