MMPC-005 Solved Assignment

Q1. How does the questionnaire approach help in collecting primary data, and what makes a questionnaire “good”?

Questionnaire method (idea and working)

The questionnaire method is a common way to collect primary data by preparing a structured set of relevant questions and recording responses from selected respondents. It can be administered through personal interviews (face-to-face), mail questionnaires, or telephonic questioning, depending on cost, time, and geographical spread of respondents. In practice, it is considered efficient and fast, but it also has limitations—especially when questions are sensitive (e.g., income or personal details) or when respondents interpret questions differently, which can reduce accuracy.

Essentials of a good questionnaire (design checklist)

• Include a covering letter: State the purpose of the study, assure confidentiality, and motivate respondents to cooperate.
• Keep the number of questions to the minimum: Shorter questionnaires usually get better completion; as a rough guide, keeping questions within a manageable range and dividing into parts if the questionnaire becomes long improves clarity.
• Use simple, short, and unambiguous wording: Avoid vague terms; if a term can be interpreted differently, specify categories clearly (e.g., levels of education rather than “literate”).
• Avoid overly sensitive/personal questions: If such questions are unavoidable, provide strong confidentiality assurance.
• Avoid questions requiring calculations: Frame questions so respondents can answer directly without computing values.
• Maintain logical arrangement: Start with easy introductory questions, place the most important questions in the middle, and end with lighter questions to leave a positive overall impression.
• Add cross-checks and footnotes where needed: Cross-check questions improve reliability; footnotes clarify boundary cases (e.g., exactly Rs. 2,000 in a class interval).
• Pre-test (pilot survey) before final use: Pre-testing helps identify problems like inconsistencies, repetitions, or irrelevant questions; revision and re-testing can improve reliability.

Practical, experience-based tips (how students can apply this)

• Decide the purpose first: If you are not clear on what decision the data should support, you will end up with unnecessary questions and weak responses.
• Prefer structured responses where possible: Multiple-choice/Yes–No formats reduce ambiguity and simplify analysis; keep open-ended questions only where essential.
• Write questions the respondent can answer confidently: If respondents must guess, the data quality will suffer—pre-testing quickly exposes such issues.

Q2. Why is measuring variability important for managerial decision-making?

Why “average” alone is not enough

In managerial work, the average (mean) may hide instability. Two alternatives can have the same mean performance but very different consistency. Measures of variation (dispersion) quantify how widely observations spread around an average, which helps a manager judge reliability and risk rather than relying only on central tendency.

Managerial uses of variability (decision-oriented)

• Risk and uncertainty assessment: Dispersion measures (especially standard deviation) are routinely interpreted as a proxy for risk in many business settings—higher dispersion generally means higher uncertainty around expected outcomes.
• Comparing stability across alternatives: When comparing two series with different means, the coefficient of variation helps compare relative variability and identify which option is more consistent.
• Operational control and consistency: In quality and process contexts, variability alerts managers to instability even if average performance looks acceptable.

How a manager would use this in real decisions

• If two suppliers quote similar average delivery times, the supplier with lower variability is typically easier to plan around (fewer emergency buffers, fewer stockouts).
• If two investment choices have similar average returns, the one with lower dispersion is usually preferred by risk-averse decision makers, because outcomes fluctuate less.

Q3. A stock has odds against going up of 2:1, and odds in favour of staying the same of 1:3. What is the probability it will go down?

Step 1: Convert odds into probabilities

“Odds against Up = 2:1” means there are 2 chances against for 1 chance in favour, so the probability of Up is 1 divided by (2+1). “Odds in favour of Same = 1:3” means 1 chance in favour for 3 chances against, so the probability of Same is 1 divided by (1+3).

$$ P(\text{Up})=\frac{1}{2+1}=\frac{1}{3},\qquad P(\text{Same})=\frac{1}{1+3}=\frac{1}{4} $$

Step 2: Use the fact that outcomes are mutually exclusive and collectively exhaustive

If the price can only go Up, remain the Same, or go Down, then these probabilities must add to 1. So:

$$ P(\text{Down}) = 1 – P(\text{Up}) – P(\text{Same}) = 1 – \frac{1}{3} – \frac{1}{4} = 1 – \frac{7}{12} = \frac{5}{12} $$

Answer

$$ P(\text{Down})=\frac{5}{12}\approx 0.4167 $$

Q4. If outcome probabilities are not available, what criteria can be used for decision-making?

Decision-making under uncertainty (probabilities unknown)

When probabilities cannot be assessed, decision theory suggests using rule-based criteria that depend on payoffs (or costs) rather than probability-weighted expected values. Commonly used criteria include:

• Pessimism criterion (Maximin): Identify the minimum payoff for each alternative, then choose the alternative with the highest of these minimum payoffs. This suits a very cautious decision maker.
• Optimism criterion (Maximax): Identify the maximum payoff for each alternative, then choose the alternative with the largest maximum payoff. This suits a highly optimistic decision maker.
• Regret criterion (Minimax Regret): Convert the payoff table into a regret (opportunity loss) table, then choose the alternative that minimizes the maximum regret.
• Laplace criterion (Equal likelihood): Treat all states of nature as equally likely and choose the alternative with the highest average payoff (or lowest average cost).
• Hurwicz criterion (weighted optimism): Use a coefficient of optimism (often denoted by α) to compute a weighted value between the best and worst payoff for each alternative, then select the best weighted result.

Practical guidance for choosing a criterion

• If survival (avoiding worst-case loss) is the priority, managers often lean toward Maximin.
• If the organization is pursuing aggressive growth opportunities, Maximax may match the strategy.
• If accountability is high and managers want to avoid “I chose the option that looks worst in hindsight,” Minimax Regret is often practical.
• If no strong view exists about which state is more likely, Laplace provides a neutral starting point.
• If management wants a tunable balance between caution and optimism, Hurwicz is suitable.

Q5. A supplier claims higher hardness: μ = 20.25, σ = 2.5, n = 100, sample mean = 20.50. Test whether the claim is acceptable.

Step 1: Set up hypotheses (right-tailed test)

$$ H_0:\mu \le 20.25 \qquad\text{vs.}\qquad H_1:\mu > 20.25 $$

Step 2: Use a z-test (population standard deviation known)

Since the hardness is normal (and n is large) and σ is known, we use the normal-based test procedure with standard error σ/√n.

Step 3: Compute the test statistic

$$ z=\frac{\bar{x}-\mu_0}{\sigma/\sqrt{n}} =\frac{20.50-20.25}{2.5/\sqrt{100}} =\frac{0.25}{0.25} =1.00 $$

Step 4: Critical value and decision rule (5% significance, right tail)

At α = 0.05 for a one-tailed test, the critical z-value is 1.645, so the critical sample-mean cut-off is:

$$ \bar{x}_{\text{critical}} =\mu_0 + 1.645\left(\frac{\sigma}{\sqrt{n}}\right) =20.25 + 1.645(0.25) =20.66125 $$

Reject H₀ only if (\bar{x}) is at least 20.66125.

Step 5: Conclusion

The observed (\bar{x}=20.50), which is below 20.66125 (and equivalently z = 1.00 is below 1.645). Therefore, at the 5% significance level, the sample evidence is not strong enough to reject H₀. The supplier’s claim of “higher mean hardness” is not supported strongly enough by this sample.

Managerial interpretation (errors and costs)

• Type I error (α): Switching to the new supplier even though the true mean hardness is not higher.
• Type II error (β): Not switching even though the supplier truly provides higher mean hardness.

Because α and β reflect different business consequences, the significance level is typically selected after considering the relative costs of these two errors.