Basic Statistics · Unit 9
Statistical Hypothesis Testing and Applications
Exam-focused notes for Statistical Hypothesis Testing and Applications (Basic Statistics, STA154): what the TU syllabus asks and how it has actually been tested, with 2 solved past questions from this unit.
What this unit covers
- Hypothesis testing concepts
- Type I and Type II errors
- Test selection based on measurement scale
- Application of statistics in IT systems
- Quality control and reliability analysis
- Expected value and decision making
Expected value and decision making
A tech support team handles the following number of customer queries (X) per hour along with their probabilities. Find the expected number and variance of queries handled per hour.
$$\begin{array}{|c|ccccc|}\hline X & 0 & 1 & 2 & 3 & 4 \ \hline P(X) & 0.10 & 0.20 & 0.30 & 0.25 & 0.15 \ \hline \end{array}$$
[5]
X 0 1 2 3 4 ------------------ P(X) 0.10 0.20 0.30 0.25 0.15 Check: $\sum P(X) = 0.10 + 0.20 + 0.30 + 0.25 + 0.15 = 1.00$ ✓ (valid distribution) --- $$E(X) = \sum X \cdot P(X)$$ X P(X) X·P(X) ----------------- 0 0.10 0.00 1 0.20 0.20 2 0.30 0.60 3 0.25 0.75...
Full solved answer →A jewelry dealer is interested in purchasing gold necklace for which probabilities are 0.18, 0.22, 0.33 and 0.27 respectively that it will be sold for a profit of Rs. 5000, Rs. 8000, 6000 and sell for a loss of Rs. 3000. Find expected profit and variance of profit. [5]
- Outcomes (profit/loss): Rs. 5000, Rs. 8000, Rs. 6000, and a loss of Rs. 3000 (i.e. $-3000$) - Probabilities: 0.18, 0.22, 0.33, 0.27 Let $X$ = profit in Rs. $X$ 5000 8000 6000 -3000 ------------------------------ $P(X)$ 0.18 0.22 0.33 0.27 Check: $0.18 + 0...
Full solved answer →Make Unit 9 stick
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