MKT 212 – Business Statistics I OSUNTECHCOLLEGE 2023/2024 First Semester Examination

ANSWER

Question 1a:

1. Lichen: A symbiotic association between a fungus and an alga or cyanobacterium. Example: Cladonia rangiferina (reindeer lichen).
2. Lentic Water: Still water bodies, such as lakes, ponds, and swamps. Example: Lake Victoria.
3. Lotic Water: Flowing water bodies like rivers and streams. Example: River Nile.
4. Bacteriophage: A virus that infects and replicates within bacteria. Example: T4 bacteriophage.
5. Chemoautolithotroph: Organisms that obtain energy by oxidizing inorganic compounds. Example: Nitrosomonas.

Question 1b:

Zones in Marine Water Habitat:

1. Intertidal Zone – Area between high and low tide.
2. Neritic Zone – Shallow waters extending from low tide to the continental shelf.
3. Oceanic Zone – Deep open ocean beyond the continental shelf.
4. Benthic Zone – Ocean floor habitat.
5. Abyssal Zone – Deep ocean regions with extreme conditions.

Question 2a:

Colony Morphology Traits:

1. Size
2. Shape (circular, irregular, filamentous)
3. Margin (smooth, lobate, serrated)
4. Elevation (flat, raised, convex)
5. Texture (dry, mucoid, rough)
6. Color (pigmentation)
7. Opacity (opaque, translucent, transparent)

Question 2b:

Units of Measurement in Bacteriology:

1. Micrometer (µm)
2. Nanometer (nm)
3. Colony-forming unit (CFU)

Question 2c:

Basic Dyes in Bacteriology:

1. Crystal Violet
2. Safranin
3. Methylene Blue
4. Malachite Green

Question 3a:

Microorganisms in the Nitrogen Cycle:

1. Nitrogen Fixation: Rhizobium, Azotobacter convert nitrogen gas into ammonia.
2. Nitrification: Nitrosomonas converts ammonia to nitrite, Nitrobacter converts nitrite to nitrate.
3. Assimilation: Plants absorb nitrates from the soil.
4. Ammonification: Decomposers convert organic nitrogen into ammonia.
5. Denitrification: Pseudomonas converts nitrates back into nitrogen gas.

Here are the answers to the remaining questions:

QUESTION FOUR

(a) Probability of Machine Q Producing a Defective Item

Given:

• Machine P: 20% production, 2.0% defective
• Machine Q: 30% production, 1.75% defective
• Machine R: 10% production, 2.5% defective

Using Bayes’ Theorem:

P(Q∣D)=P(D∣Q)P(Q)P(D)P(Q|D) = \frac{P(D|Q)P(Q)}{P(D)}

Where:

• P(Q)=0.30P(Q) = 0.30
• P(D∣Q)=0.0175P(D|Q) = 0.0175
• P(D)=(0.20×0.02)+(0.30×0.0175)+(0.10×0.025)P(D) = (0.20 \times 0.02) + (0.30 \times 0.0175) + (0.10 \times 0.025)

=0.004+0.00525+0.0025=0.01175= 0.004 + 0.00525 + 0.0025 = 0.01175 P(Q∣D)=0.005250.01175=0.4468≈44.68%P(Q|D) = \frac{0.00525}{0.01175} = 0.4468 \approx 44.68\%

(b) Systematic Sampling Technique

• Given: 160 managers
• Select every k=16020=8k = \frac{160}{20} = 8th manager
• Start from Manager 059
• The selected managers will be 59, 67, 75, 83, 91, 99, 107, 115, 123, 131, 139, 147, 155, 163, 171, 179, 187, 195, 203, 211

QUESTION FIVE

(a) What is a Statistical Variable?

A statistical variable is a characteristic that can take on different values in a dataset. It can be qualitative (categorical) or quantitative (numerical).

(b) Methods of Gathering Primary Data

1. Mail Questionnaire – Sending structured questions via mail to respondents.
2. Telephone Interview – Collecting data by calling respondents.
3. Personal Interview – Face-to-face questioning for more detailed responses.
4. Experiment Method – Conducting controlled tests to gather empirical data.

(c) Difference Between Data and Information

• Data: Raw facts and figures (e.g., exam scores: 45, 78, 89).
• Information: Processed data that provides meaning (e.g., “The average score is 70%”).

QUESTION SIX

(a) Five Qualities of a Good Table

1. Title – Clearly describes the table content.
2. Row & Column Labels – Proper headings for clarity.
3. Units of Measurement – Indicated where necessary.
4. Legibility – Easy to read and interpret.
5. Source – Where the data originates from.

(b) Median and Mode of Auto Parts Prices

Given Data:

(i) Median Calculation
Total items sold = 458
Median position = (458 + 1) / 2 = 229.5

• Cumulative frequency up to 50-59 is 228
• Cumulative frequency up to 60-69 is 328
• Median falls in 60-69 range

Using Median Formula:

Median=L+(N2−Ff)×h\text{Median} = L + \left(\frac{\frac{N}{2} – F}{f}\right) \times h

Where:

• L=60L = 60 (lower boundary)
• N/2=229.5N/2 = 229.5
• F=228F = 228 (cumulative frequency before class)
• f=100f = 100 (frequency of median class)
• h=10h = 10 (class width)

Median=60+(229.5−228100)×10\text{Median} = 60 + \left(\frac{229.5 – 228}{100}\right) \times 10 =60+(1.5/100×10)=60+0.15=60.15= 60 + (1.5/100 \times 10) = 60 + 0.15 = 60.15

Median ≈ 60.2 million

(ii) Mode Calculation

• Modal class = 50-59 (highest frequency = 120)
• Using Mode Formula:

Mode=L+(f1−f0(2f1−f0−f2))×h\text{Mode} = L + \left(\frac{f_1 – f_0}{(2f_1 – f_0 – f_2)}\right) \times h

Where:

• L=50L = 50 (lower boundary)
• f1=120f_1 = 120 (modal frequency)
• f0=60f_0 = 60 (preceding frequency)
• f2=100f_2 = 100 (following frequency)
• h=10h = 10 (class width)

Mode=50+(120−60(2×120−60−100))×10\text{Mode} = 50 + \left(\frac{120 – 60}{(2 \times 120 – 60 – 100)}\right) \times 10 =50+(6080)×10= 50 + \left(\frac{60}{80}\right) \times 10 =50+7.5=57.5= 50 + 7.5 = 57.5

Mode ≈ 57.5 million

QUESTION SEVEN

(a) Construct a Frequency Distribution Table

Using class intervals like 128-137, 138-147, 148-157, etc., and tallying data accordingly.

(b) Cumulative Frequency Curve (Ogive)

• Compute cumulative frequencies from part (a).
• Plot cumulative frequency against class boundaries.
• Draw a smooth curve.

SECTION B

QUESTION ONE

(a) Pie Chart Calculation

Convert given income to degrees using:

Sector Angle=IncomeTotal Income×360∘\text{Sector Angle} = \frac{\text{Income}}{\text{Total Income}} \times 360^\circ

(b) Range of Regional Income in Southwest

Range=Maximum Income−Minimum Income=752−255=497\text{Range} = \text{Maximum Income} – \text{Minimum Income} = 752 – 255 = 497

QUESTION TWO

(a) Regression Equation

Using:

Y=a+bXY = a + bX

Compute aa and bb using least squares regression.

(b) Predict Sales for X=7.8X = 7.8

Substitute X=7.8X = 7.8 into regression equation.

QUESTION THREE

(a) Component Bar Chart for Livestock Slaughtered

• Plot cattle, goats, and pigs as grouped bars for each local government.

(b) Five Reasons for Using Statistics in an Organization

1. Decision Making – Helps in planning and forecasting.
2. Performance Analysis – Evaluates business performance.
3. Quality Control – Ensures product quality.
4. Market Research – Helps understand customer behavior.
5. Risk Assessment – Identifies and mitigates risks.