Business Analytics · Quiz 1 · Jan 2025

**1. Recall what a pie chart encodes:** Its slices represent proportions of a common total. **2. Compare the proposed purposes:** Outlier detection, trends and numerical relationships each require different visual encodings; none of those is the primary purpose of a pie chart. **Answer: D — None of these.** A: **Incorrect:** Outliers are clearer in box plots or dot plots. B: **Incorrect:** Trends are clearer in line charts. C: **Incorrect:** Relationships between numerical variables are clearer in scatter plots. D: **Correct:** None lists the parts-of-a-whole purpose of a pie chart.

**1. Partition by starter:** P(BCM)=0.25, P(PT)=0.40 and P(MP)=0.35. Treat eater types and starter choices as mutually exclusive categories as instructed. **2. Calculate rice-eater probability:** BCM has no rice eaters; PT contributes \(0.40(0.40)=0.16\); MP contributes \(0.35(0.50)=0.175\). Thus P(Rice)=0.335. **3. Convert to customers:** \(1000(0.335)=335.00\). **Answer: 335.00.**

**1. Use the starter share:** One quarter of customers order BCM, independent of whether their eater category is subsequently specified. **2. Multiply by footfall:** \(4000(0.25)=1000.00\) expected BCM orders. **Answer: 1000.00.**

**1. Partition by starter:** P(BCM)=0.25, P(PT)=0.40 and P(MP)=0.35. Treat eater types and starter choices as mutually exclusive categories as instructed. **2. Calculate other-eater shares within each starter:** BCM leaves 1−0.30−0.60=0.10; PT leaves 1−0.40−0.20−0.20=0.20; MP leaves 1−0.50−0.40=0.10. **3. Apply total probability and footfall:** \(P(Other)=0.25(0.10)+0.40(0.20)+0.35(0.10)=0.14\). Thus \(10000(0.14)=1400.00\). **Answer: 1400.00.**

**1. Calculate joint other-eater probabilities:** PT contributes 0.40(0.20)=0.08; BCM contributes 0.25(0.10)=0.025; MP contributes 0.35(0.10)=0.035. Total P(Other)=0.14. **2. Condition on the observed category:** Given an other eater, starter probabilities are \(P(PT\mid Other)=0.08/0.14\approx0.5714\), BCM≈0.1786 and MP=0.25. PT is the most likely. **Answer: A — PT.** A: **Correct:** Its conditional probability is largest, approximately 0.5714. B: **Incorrect:** Its conditional probability is only about 0.1786. C: **Incorrect:** Its conditional probability is 0.25, below PT. D: **Incorrect:** The question explicitly supplies the observation; this distractor does not answer the probability comparison.

**1. Apply the explicitly stipulated equal-area model:** There are four bins and ten observations, so each bin has probability 1/4 and expected count 2.5. **2. Count the observed values:** The listed readings give O=(0,0,7,3): seven are above 70 and at most 90, and three are above 90 and at most 100. **3. Read Bin-2 expectation:** \(E_2=10(1/4)=2.50\). **Answer: 2.50.** **Convention note:** The printed cutoffs are not equal-probability bins of N(50,10²). Under that literal normal distribution, P(50<X≤70)≈0.47725 and E2≈4.77. The answer 2.50 follows the passage’s explicit equal-area instruction instead.

**1. Count categories:** The stipulated equal-probability test has four bins. Its cell probabilities are specified, not estimated. **2. Subtract the total-count constraint:** \(df=4-1=3\), entered as 3.00. **Answer: 3.00.** **Convention note:** This is the nominal df under the equal-area instruction. The stated N(50,10²) does not give those equal bin probabilities, and the small expected counts make the asymptotic reference distribution unreliable.

**1. Use the nonrejection rule:** With p=0.85, do not reject H0 when α<0.85 under the usual reject-if-p≤α rule. **2. Compare the choices:** α=0.15 satisfies this condition; α=0.90 does not. Not every value in [0,1] permits nonrejection. **Answer: B — 0.15.** A: **Incorrect:** 0.85≤0.90 triggers rejection. B: **Correct:** 0.85>0.15 gives nonrejection. C: **Incorrect:** Values above or equal to 0.85 do not satisfy the usual nonrejection condition. D: **Incorrect:** The given p-value already provides the required information.

**1. Identify both price–demand points:** The old price is 45−5=40 with demand 300; the new point is (45,100). **2. Fit the linear demand curve:** Its slope is (100−300)/(45−40)=−40. Substituting (40,300) gives intercept 300+40(40)=1900, so \(D(p)=1900-40p\). **3. Report the intended response coefficient:** Demand falls by 40 litres for each additional rupee per litre, so the positive slope magnitude is 40.00. **Answer: 40.00.** **Convention note:** The key calls the slope coefficient “elasticity.” True dimensionless elasticity is not constant: ε(p)=40p/(1900−40p), equal to 5.33 at p=40 and 18.00 at p=45. Midpoint arc elasticity across the stated change is 8.50. Thus 40 is price sensitivity in units, not conventional percentage elasticity.

**1. Identify both price–demand points:** The old price is 45−5=40 with demand 300; the new point is (45,100). **2. Fit the linear demand curve:** Its slope is (100−300)/(45−40)=−40. Substituting (40,300) gives intercept 300+40(40)=1900, so \(D(p)=1900-40p\). **3. Read demand at zero price:** \(D(0)=1900.00\), the linear model’s market size. **Answer: 1900.00.**

**1. Identify both price–demand points:** The old price is 45−5=40 with demand 300; the new point is (45,100). **2. Fit the linear demand curve:** Its slope is (100−300)/(45−40)=−40. Substituting (40,300) gives intercept 300+40(40)=1900, so \(D(p)=1900-40p\). **3. Solve for zero demand:** \(0=1900-40p\), giving satiating price \(p=1900/40=47.50\). **Answer: 47.50.**

**1. Identify both price–demand points:** The old price is 45−5=40 with demand 300; the new point is (45,100). **2. Fit the linear demand curve:** Its slope is (100−300)/(45−40)=−40. Substituting (40,300) gives intercept 300+40(40)=1900, so \(D(p)=1900-40p\). **3. Assess conventional elasticity:** At the old price its magnitude is 40(40)/300≈5.33; at the new price it is 40(45)/100=18. Both exceed 1, and midpoint arc elasticity is also 8.50>1, so demand over this range is elastic. **4. Separate price and income effects:** Luxury/necessity classifications require income-elasticity information, which is absent. **Answer: A — A — elastic.** A: **Correct:** The percentage demand response exceeds the percentage price change over the given range. B: **Incorrect:** Its elasticity magnitude is above 1 rather than below 1. C: **Incorrect:** Price responsiveness alone does not establish a luxury good. D: **Incorrect:** Price responsiveness alone does not establish a necessity by income elasticity. E: **Incorrect:** There is enough information to identify elastic demand over the stated price range.

**1. Read the 2×2 observed table:** Chennai has (A,B)=(200,145), total 345; Mumbai has (600,255), total 855. Column totals are A=800 and B=400; N=1200. **2. Compute independence expectations:** \(E_{ij}=R_iC_j/N\) gives Chennai (230,115) and Mumbai (570,285). **3. Read the requested expectation:** \(E_{Chennai,B}=345(400)/1200=115.00\). **Answer: 115.00.**