Stats Test 1 Review

Here are the requested flashcards based on the information provided:

Flashcard 1: Identifying Population vs. SampleQuestion:A researcher surveys 300 randomly selected households in Austin to determine the average commuting time. Identify the population and sample.Concept:

• Population: The entire group being studied.

• Sample: A subset of the population used for analysis.Answer:

• Population: All people in Austin.

• Sample: 300 randomly selected households.

Flashcard 2: Mean, Median, and ModeQuestion:Find the mean, median, and mode for the dataset:2, 4, 6, 7, 8, 10, 12, 15, 19, 25Formulas:

• Mean (Average): (\bar{x} = \frac{\sum x_i}{n})

• Median: Middle value when ordered

• Mode: Most frequent value(s)Solution:

• Mean: (\bar{x} = \frac{2 + 4 + 6 + 7 + 8 + 10 + 12 + 15 + 19 + 25}{10} = 10.8)

• Median: Middle value → (7 + 8)/2 = 7.5

• Mode: No mode (no repeating values)

Flashcard 3: Probability - Union of Two EventsQuestion:A school survey finds:

• 25% of students play basketball

• 30% play soccer

• 10% play bothFind the probability of a student playing either sport.Formula:(P(A ∪ B) = P(A) + P(B) - P(A ∩ B))Solution:(P(Basketball ∪ Soccer) = 0.25 + 0.30 - 0.10 = 0.45)

Flashcard 4: Finding Standard DeviationQuestion:If variance = 11, find the standard deviation.Formula:(σ = \sqrt{variance})Solution:(σ = \sqrt{11} = 3.317)

Flashcard 4: Finding Standard DeviationQuestion:If variance = 11, find the standard deviation.Formula:σ = √(variance)Solution:σ = √11 ≈ 3.317

Flashcard 5: Interquartile Range & OutliersQuestion:Find Q1, Q3, range, and IQR for:2, 4, 6, 7, 8, 10, 12, 15, 19, 25Formulas:IQR = Q3 - Q1Outliers: Values < Q1 - 1.5(IQR) or > Q3 + 1.5(IQR)Solution:Q1 = 6, Q3 = 15Range = 25 - 2 = 23IQR = 15 - 6 = 9No outliers

Flashcard 6: Probability - Union of Two EventsQuestion:A school survey finds:25% play basketball, 30% play soccer, 10% play both. Find P(Basketball ∪ Soccer).Formula:P(A ∪ B) = P(A) + P(B) - P(A ∩ B)Solution:P(Basketball ∪ Soccer) = 0.25 + 0.30 - 0.10 = 0.45

Flashcard 7: Probability Using CombinationsQuestion:A store has 12 laptops, 8 are out of stock. A customer randomly selects 4. Find P(all 4 are out of stock).Formula:P = (Number of ways to choose 4 out of 8) / (Number of ways to choose 4 out of 12)Solution:P = 70 / 495 ≈ 0.141

Flashcard 8: Conditional ProbabilityQuestion:Given P(A) = 0.33, P(B) = 0.22, and P(A ∪ B) = 0.45, find P(A | B).Formula:P(A | B) = P(A ∩ B) / P(B)Solution:P(A ∩ B) = P(A) + P(B) - P(A ∪ B) = 0.33 + 0.22 - 0.45 = 0.10P(A | B) = 0.10 / 0.22 ≈ 0.455

Flashcard 9: Probability Distribution Mean & VarianceQuestion:Find mean and variance from:X0 1 2 3 4P(X)0.10 0.25 0.35 0.20 0.10Formulas:Mean: E(X) = Σ [X * P(X)]Variance: Var(X) = Σ [(X - μ)² * P(X)]Solution:Mean = 1.95Variance ≈ 1.248

Flashcard 10: Binomial ProbabilityQuestion:A restaurant knows 35% of customers order dessert. In a sample of 30, find P(exactly 12 order dessert).Formula:Use binomial formula or dbinom function in RSolution:P(X = 12) ≈ 0.125

Flashcard 11: Proving IndependenceQuestion:Given P(A) = 0.33, P(B) = 0.22, and P(A ∩ B) = 0.10, are A and B independent?Formula:P(A and B are independent if P(A) * P(B) = P(A ∩ B)Solution:P(A) * P(B) = 0.33 * 0.22 = 0.0726Since 0.0726 ≠ 0.10, A and B are not independent.

Flashcard 1: Identifying Population vs. SampleQuestion:A researcher surveys 300 randomly selected households in Austin to determine the average commuting time. Identify the population and sample.Concept:

• Population: The entire group being studied.

• Sample: A subset of the population used for analysis.Answer:

• Population: All people in Austin.

• Sample: 300 randomly selected households.

Flashcard 2: Types of DataQuestion:Classify the following as categorical or quantitative. If quantitative, state whether it's discrete or continuous.

• Number of books read in a year

• Weight of apples harvestedConcept:

• Categorical: Describes qualities or characteristics.

• Quantitative: Numerical values, can be discrete (countable) or continuous (measurable).Answer:

• Number of books: Quantitative, discrete

• Weight of apples: Quantitative, continuous

Flashcard 3: Mean, Median, and ModeQuestion:Find the mean, median, and mode for the dataset: 2, 4, 6, 7, 8, 10, 12, 15, 19, 25Formulas:

• Mean: (\bar{x} = \frac{\sum x_i}{n})

• Median: Middle value when ordered

• Mode: Most frequent value(s)Solution:

• Mean: (\bar{x} = \frac{2 + 4 + 6 + 7 + 8 + 10 + 12 + 15 + 19 + 25}{10} = 10.8)

• Median: Middle value → (7 + 8)/2 = 7.5

• Mode: No mode (no repeating values)

Flashcard 4: Finding Standard DeviationQuestion:If variance = 11, find the standard deviation.Formula:(σ = \sqrt{variance})Solution:(σ = \sqrt{11} ≈ 3.317)

Flashcard 5: Identifying Binomial vs. Geometric ProbabilityConcept:

• Binomial Probability: Used when there are n independent trials, each with two possible outcomes (success/failure), and we are interested in the number of successes.

• Geometric Probability: Used when there are repeated independent trials, and we are interested in the first success.How to Identify:

• If the question asks how many successes in n trials, use binomial.

• If the question asks when the first success occurs, use geometric.

Flashcard 6: Step-by-Step Binomial ProbabilityQuestion:A restaurant knows 35% of customers order dessert. In a sample of 30, find P(exactly 12 order dessert).Formula:(P(X = k) = \binom{n}{k} p^k (1-p)^{n-k})Step-by-Step Solution:

• Identify values:

  • n (total trials): 30

  • k (desired successes): 12

  • p (probability of success): 0.35

  • (probability of failure): 0.65

• Compute binomial coefficient:(\binom{30}{12} = 125,970)

• Compute probability:P = (\binom{30}{12} (0.35^{12}) (0.65^{18}))

• Use a calculator or R function: dbinom(12, 30, 0.35)Answer:≈ 0.125

Flashcard 7: Step-by-Step Geometric ProbabilityQuestion:The probability a person orders dessert is 0.35. Find P(first order on the 5th customer).Formula:(P(X = k) = (1-p)^{k-1} p)Step-by-Step Solution:

• Identify values:

  • k (first success on 5th trial): 5

  • p (probability of success): 0.35

  • (probability of failure): 0.65

• Compute probability:P = (0.65)^{4} (0.35)

• Use a calculator or R function: dgeom(4, 0.35)Answer:≈ 0.089