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Course Code : MMPC-005
Course Title : Quantitative Analysis For Managerial Applications

1.Describe briefly the questionnaire method of collecting primary data. State the essentials of a good questionnaire.

Answer:

The questionnaire method of collecting primary data is a widely used research tool where respondents are provided with a set of structured questions to gather specific information. This method is effective for collecting large amounts of data in a systematic and efficient manner. Questionnaires can be administered in various forms such as paper-based, online, or via phone interviews. The method is particularly useful for surveys, market research, and social science studies, as it allows researchers to collect data from a large number of individuals relatively quickly and at a lower cost.

The primary advantage of using questionnaires is that they provide standardized responses, which makes it easier to analyze and compare data. Additionally, they allow for anonymity, which may encourage more honest and unbiased responses. However, the method’s effectiveness depends heavily on the design of the questionnaire.

Essentials of a Good Questionnaire:

Clear Objectives: A good questionnaire must have well-defined objectives that align with the research goals. The questions should be crafted to gather relevant and targeted information that helps answer the research questions.
Simple and Clear Language: Questions should be straightforward, avoiding jargon, technical terms, or complex sentence structures. This ensures that respondents from various backgrounds can easily understand and answer the questions accurately.
Relevance: Every question should be directly relevant to the research objectives. Irrelevant or off-topic questions can confuse respondents and lead to unreliable data.
Question Types: A mix of question types, such as multiple-choice, Likert scales, open-ended, and ranking questions, can help gather both quantitative and qualitative data. The questions should be designed to avoid leading responses or bias.
Logical Flow: The questions should be organized in a logical sequence, with general questions leading into more specific ones. This ensures the questionnaire flows smoothly and is easier for respondents to follow.
Brevity: The questionnaire should be as concise as possible. Long and time-consuming questionnaires can discourage respondents from completing them and may reduce response rates.
Neutrality: The language used in questions should be neutral and not lead the respondent towards a particular answer. Avoid emotionally charged or biased wording that may influence responses.
Pilot Testing: Before distributing the questionnaire widely, it’s essential to pilot test it on a small sample. This helps identify any unclear or confusing questions, ensuring the final version is effective.

2. Discuss the importance of measuring variability for managerial decision-making.

Answer:

Measuring variability is a crucial aspect of data analysis in managerial decision-making. Variability refers to how spread out or dispersed data points are in a dataset. In other words, it reflects the degree to which data values differ from the mean or average. Common measures of variability include range, variance, and standard deviation. Understanding and measuring variability helps managers assess risk, predict outcomes, and make informed decisions in a dynamic business environment.

Importance of Measuring Variability for Managerial Decision-Making:

Assessing Risk and Uncertainty: Variability provides insight into the risk and uncertainty within a business environment. If the variability is high, it suggests greater unpredictability, which can influence decisions regarding investment, budgeting, and resource allocation. For instance, if a company is unsure about the demand for a new product, measuring variability in historical sales data can help estimate the range of potential outcomes and inform the company’s strategy.
Setting Realistic Expectations: Understanding the extent of variability allows managers to set more realistic goals and performance expectations. For example, if sales figures show high variability, it may be unrealistic to expect consistent growth year after year. Recognizing this variability enables managers to set more flexible and attainable targets, improving performance evaluation and employee motivation.
Resource Allocation: Variability data helps managers allocate resources more efficiently. For example, if variability in supply chain delivery times is high, managers may choose to stock more inventory to mitigate the risk of stockouts. Conversely, if variability is low and operations are stable, resources can be optimized for greater efficiency.
Improving Forecasting Accuracy: Accurate forecasting relies on understanding variability. If variability is low, forecasts are generally more accurate, and managers can rely more heavily on historical data to predict future trends. On the other hand, high variability may require more sophisticated forecasting models that incorporate uncertainty, helping managers prepare for a wider range of potential outcomes.
Identifying Process Improvements: Variability can highlight areas of inefficiency or inconsistency in operations. For instance, if there is significant variability in production costs, managers may investigate underlying factors such as machinery malfunctions, employee training, or supply chain disruptions. Reducing variability in these areas can lead to smoother operations, cost reductions, and higher overall efficiency.
Strategic Decision-Making: Managers often need to make strategic decisions under conditions of uncertainty. By understanding the variability in key business metrics, such as sales, profits, and customer satisfaction, they can make more informed and effective decisions about expansion, product launches, or market entry.

3 An investment consultant predicts that the odds against the price of a certain stock will go up during the next week are 2:1 and the odds in favour of the price remaining the same are 1:3. What is the probability that the price of the stock will go down during the next week?

Answer:

To determine the probability that the price of the stock will go down during the next week, we need to carefully analyze the given odds. The consultant has provided two sets of odds:

Odds against the price going up: 2:1.
Odds in favor of the price remaining the same: 1:3.

Understanding the Odds:

Before diving into the probability calculations, it’s important to first understand what these odds represent.

Odds against the price going up (2:1) means that for every 3 possible outcomes (2 + 1), 2 of those outcomes are the price going down, and 1 outcome is the price going up. Therefore, the probability of the price going up is:

P(Going Up)=1 / 2+1 = 1/3

This is the probability of the price going up.

Odds in favor of the price remaining the same (1:3) means that for every 4 possible outcomes (1 + 3), 1 of those outcomes is the price remaining the same, and 3 outcomes are the price either going up or down. Therefore, the probability of the price remaining the same is:

This is the probability of the price remaining the same.

Calculating the Probability of the Price Going Down:

The total probability for all possible outcomes must sum to 1. We already know the probabilities for the price going up and remaining the same:

Let’s denote the probability of the price going down as . Since the sum of probabilities for all possible outcomes must equal 1, we can write:

P(Going Up) + P(Remaining Same) + P(Going Down) = 1

Substitute the known values:

1 / 3 + 1/ 4 + P(Going Down)=1

To solve for , first find a common denominator. The least common denominator of 3 and 4 is 12. Rewriting the fractions:

1 / 3 = 4 / 12, 1 / 4 = 3 / 12

Now substitute these values back into the equation:

4 / 12 + 3 / 12 +P(Going Down)=1

Combine the fractions:

7 / 12 + P(Going Down)=1

Subtract from both sides:

P(Going Down)=1− 7 / 12 =12 / 12 − 7 / 12 = 5 / 12

4 In practice, we find situations where it is not possible to make any probability assessment. What criterion can be used in decision-making situations where the probabilities of outcomes are unknown?

Answer: 

In real-world decision-making, there are often situations where the probabilities of possible outcomes are unknown, making traditional probabilistic models of decision-making unsuitable. In such cases, decision-makers need alternative approaches to guide their decisions under uncertainty. Several criteria can be applied in decision-making situations where probabilities cannot be assessed. These include the Maximin, Maximax, Minimax Regret, Hurwicz, and Laplace criteria. Each approach represents a different strategy for managing risk and uncertainty.

1. Maximin Criterion (Pessimistic Decision Rule)

The Maximin Criterion is used by decision-makers who adopt a highly cautious or risk-averse approach. The idea behind this criterion is that in the face of uncertainty, it is safer to focus on minimizing the potential for the worst possible outcome. The decision-maker considers the worst possible outcome for each alternative and selects the one with the least damaging worst-case scenario.

How it works: For each decision option, identify the worst possible outcome. Then, select the alternative that has the highest of these worst outcomes.
Example: Suppose a company is deciding between three investment options with the following worst outcomes:
- Investment A: Worst outcome = $10,000
- Investment B: Worst outcome = $15,000
- Investment C: Worst outcome = $5,000
According to the Maximin criterion, the company would choose Investment B because its worst possible outcome ($15,000) is better than the worst outcomes of the other investments.

2. Maximax Criterion (Optimistic Decision Rule)

The Maximax Criterion is used by decision-makers who are optimistic and willing to take on more risk in hopes of achieving the best possible outcome. This criterion focuses on maximizing the best possible outcome for each alternative, assuming the most favorable scenario will occur.

How it works: For each decision alternative, identify the best possible outcome. Then, select the alternative with the highest of these best outcomes.
Example: Suppose the best outcomes for three investments are as follows:
- Investment A: Best outcome = $100,000
- Investment B: Best outcome = $80,000
- Investment C: Best outcome = $50,000
Under the Maximax criterion, the company would choose Investment A, since its best possible outcome ($100,000) is the highest.

3. Minimax Regret Criterion (Opportunity Loss Approach)

The Minimax Regret Criterion helps minimize potential regrets that could arise from making a wrong decision. Regret is defined as the difference between the outcome of the decision made and the best possible outcome that could have been achieved. The goal of this criterion is to select the option that minimizes the maximum regret.

How it works: For each alternative, calculate the regret for each possible state of nature (i.e., the difference between the outcome of that option and the best outcome for each scenario). Then, select the alternative with the smallest possible maximum regret.
Example: For three investments with varying outcomes, calculate the regret (opportunity loss) for each:
- Investment A: Best outcome = $100,000, Regret for $10,000 = $90,000
- Investment B: Best outcome = $80,000, Regret for $15,000 = $65,000
- Investment C: Best outcome = $50,000, Regret for $5,000 = $45,000
The decision-maker would select Investment C, as it minimizes the maximum regret ($45,000).

4. Hurwicz Criterion (Weighted Average Approach)

The Hurwicz Criterion is a compromise between the Maximin and Maximax criteria, suitable for decision-makers who are neither strictly optimistic nor pessimistic. It involves a weighted average of the best and worst possible outcomes for each alternative, where the decision-maker assigns a weight (denoted $α\alpha$ ) to the best outcome (ranging from 0 to 1) to reflect their degree of optimism. The remaining weight (1 – $α\alpha$ ) is assigned to the worst outcome.

How it works: For each alternative, calculate a weighted average of the best and worst outcomes. Choose the alternative with the highest weighted average.
Example: Suppose $α=0.6\alpha = 0.6$ (optimistic), and for each investment:
- Investment A: Best outcome = $100,000, Worst outcome = $10,000
- Investment B: Best outcome = $80,000, Worst outcome = $15,000
- Investment C: Best outcome = $50,000, Worst outcome = $5,000
The weighted average for Investment A would be:
$0.6 \times 100,000) + (0.4 \times 10,000) = 60,000 + 4,000 = 64,000$
Similar calculations are done for Investments B and C. The alternative with the highest weighted average is selected.

5. Laplace Criterion (Equal Probability Assumption)

The Laplace Criterion assumes that all outcomes for each alternative are equally likely when probabilities are unknown. This criterion treats all possible states of nature as equally probable and selects the alternative with the highest average outcome.

How it works: For each alternative, calculate the average of the possible outcomes, assuming equal probability for each. The alternative with the highest average is chosen.
Example: For three investments with the following outcomes:
- Investment A: $10,000, $100,000, $50,000
- Investment B: $15,000, $80,000, $60,000
- Investment C: $5,000, $50,000, $55,000
Calculate the average for each:
- Investment A: $10,000+100,000+50,0003=53,333\frac{10,000 + 100,000 + 50,000}{3} = 53,333$
- Investment B: $15,000+80,000+60,0003=51,667\frac{15,000 + 80,000 + 60,000}{3} = 51,667$
- Investment C: $5,000+50,000+55,0003=36,667\frac{5,000 + 50,000 + 55,000}{3} = 36,667$
According to the Laplace criterion, Investment A would be chosen as it has the highest average outcome.

5. A purchase manager knows that the hardness of castings from any supplier is normally distributed with a mean of 20.25 and SD of 2.5. He picks up 100 samples of castings from any supplier who claims that his castings have heavier hardness and finds the mean hardness as 20.50. Test whether the claim of the supplier is tenable.

Answer:

In this scenario, the purchase manager wants to determine whether the supplier’s claim that their castings have a higher hardness than the known population mean is valid. To do this, we can perform a hypothesis test. Here, we will use a one-sample z-test, since we are given the population mean and standard deviation, and the sample size is sufficiently large (100 samples).

Step 1: Define Hypotheses

The first step is to set up the null and alternative hypotheses:

Null Hypothesis (H₀): The supplier’s claim is not valid, meaning the true mean hardness of the castings is equal to the population mean.
$\mu = 20.25$
Alternative Hypothesis (H₁): The supplier’s claim is valid, meaning the true mean hardness of the castings is greater than the population mean. $\mu > 20.25$

This is a right-tailed test because we are testing if the sample mean is greater than the population mean.

Step 2: Given Data

Population mean ( $μ0\mu_0$ ) = 20.25
Population standard deviation ( $σ\sigma$ ) = 2.5
Sample mean ( $xˉ\bar{x}$ ) = 20.50
Sample size ( $n$ ) = 100
Significance level ( $α\alpha$ ) = 0.05 (commonly used in hypothesis testing)

Step 3: Calculate the Test Statistic

The test statistic for a z-test is given by the formula:

$\frac{\bar{x} – \mu_0}{\frac{\sigma}{\sqrt{n}}}$

Where:

$xˉ\bar{x}$ is the sample mean,
$μ0\mu_0$ is the population mean,
$σ\sigma$ is the population standard deviation,
$n$ is the sample size.

Substituting the given values:

$\frac{20.50 – 20.25}{\frac{2.5}{\sqrt{100}}}$ $\frac{0.25}{\frac{2.5}{10}} = \frac{0.25}{0.25} = 1$

Step 4: Determine the Critical Value

Since this is a one-tailed test with a significance level of 0.05, we need to find the critical z-value for $α=0.05\alpha = 0.05$ . From the standard normal distribution table, the critical z-value for a right-tailed test at a 0.05 significance level is approximately 1.645.

Step 5: Make the Decision

We compare the calculated test statistic $z = 1$ with the critical value $zcritical=1.645z_{\text{critical}} = 1.645$ :

If $z$ is greater than 1.645, we reject the null hypothesis.
If $z$ is less than or equal to 1.645, we fail to reject the null hypothesis.

Since $z = 1$ is less than 1.645, we fail to reject the null hypothesis.

MBA MMPC-005 Solved Assignments

Essentials of a Good Questionnaire:

Importance of Measuring Variability for Managerial Decision-Making: