PHFO Quantitative Analysis For Business Pre-Assessment Practice Exam

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• Which statistic measures dispersion of residuals around the regression line in simple linear regression?
• If a bar chart shows 60% Category A, 25% Category B, and 15% Category C and the sample size is 200, what are the expected counts for A, B, and C?
• Which age category accounts for the largest share of site visits?
• In simple linear regression, what is the standard error of the estimate?
• What is the formula for present value PV given FV, rate i, and periods n?
• Which type of method is break-even analysis?
• For the dataset with points (1,3) and (3,7), the least-squares regression line is y = a + b x.
• Which currency is used for the average inventory value scenario?
• Construct a 95% confidence interval for a proportion p_hat = 0.40 with n = 100 (approx using standard formula).
• In a standard normal distribution, what is P(Z ≤ 1.25)?
• Which statement is true about a perpetuity with constant payments?
• In regression analysis, high multicollinearity, indicated by high VIF, primarily affects which aspect?
• If FV = 10,000, rate 6%, n = 5, what is PV?
• If the path A-B-F-J has a total duration of 12 days, what is the duration of F?
• What is the expected annual revenue for expanding to dogs under 30 pounds, given strong economy probability 60% and weak economy probability 40%?
• Which assumption states that the residuals should be normally distributed?
• What is the addition rule for mutually exclusive events?
• State Bayes theorem formula in words.
• What is stratified sampling?
• Which statement accurately describes a sample statistic?
• A sporting goods company makes bandanas and flags. It costs $10 to produce one bandana and $12 to produce one flag. It takes 1/4 yard of material for a bandana and 1/2 yard for a flag. What is the constraint in this scenario?
• Which statement describes the difference between a population parameter and a sample statistic?
• What is the median of the data set {3, 8, 1, 6, 5}?
• Which expression equals P(X = 2) for a Poisson distribution with λ = 4?
• In regression, the standard error of the estimate measures what?
• If the variance of the residuals is constant across levels of the independent variable, the data are described as:
• Based on the blogger data, which statement best describes the behavior of new followers?
• For two mutually exclusive events A and B with probabilities P(A) = 0.3 and P(B) = 0.4, what is P(A ∪ B)?
• Which expression gives the standard error used in a 95% confidence interval for a proportion p_hat with n = 100 and p_hat = 0.40?
• How many orders per year are made under the EOQ for the taxidermist scenario?
• What does R^2 represent in regression analysis?
• In a small-sample t-test with n=9, x̄=5, s=2, H0: μ=4, α=0.05, what is the t-statistic and the conclusion?
• Which approach would be best to analyze why patients selected this ER?
• In y = α + βx with α = 1 and β = 2, what is y when x = 4?
• Which statement is true about a z-score of 0.5?
• What is the formula for the weighted mean?
• On a control chart, which observation indicates an out-of-control condition?
• State Bayes' theorem in simplest form.
• In the textile production problem, what is the objective function that minimizes production cost?
• Based on the crashing analysis, what is the maximum reduction in project time if both C and D are crashed?
• For the LP: Max Z = X1 + X2, subject to X1 + X2 ≤ 4, 2X1 + 5X2 ≤ 10, X1 ≥ 0, X2 ≥ 0, which of the following is the optimal point (X1, X2) and its Z value?
• Which statement best describes the purpose of a decision tree in decision analysis?
• Under a favorable market, which option yields the highest payoff among Large Plant, Small Plant, and Subcontracting?
• In a fair six-sided die, what is the probability of rolling an even number?
• Which regression assumption concerns a constant variance of residuals across fitted values?
• What is Monte Carlo simulation?
• With a p-value of 0.03 and alpha of 0.05, what is the decision?
• What is the standard error of the mean for a sample with s = 6 and n = 16?
• Among the four locations for the annual craft fair, which has the highest expected value based on the weather probabilities Rain 0.10, Sunny 0.60, Overcast 0.30?
• If fixed costs are $50,000 and the contribution margin per unit is $20, what is the break-even quantity?
• In a project network, which sequence of activities forms the critical path?
• What is the median of the data set {3, 7, 5, 1, 9}?
• In ANOVA, which statement best describes what the F-statistic tests?
• Which statement best describes the use of a decision tree in evaluating capacity expansion decisions?
• How many alternatives are considered in the capacity expansion decision?
• What are Type I and Type II errors in hypothesis testing?
• A three-period moving average forecast for period 4 using actuals 5, 7, 9 is what?
• If you do not know σ, what distribution do you use to form a CI for μ with small n?
• PV of an ordinary annuity with PMT = 200, i = 5%, n = 10 yields which value?
• After cancelling activity F, what is the project’s critical path?
• How do you compute the expected value of a decision with outcomes {v1, v2} and probabilities {p1, p2}?
• MAPE is defined as which of the following?
• How many orders per year are placed when EOQ is used in the mountain bikes scenario?
• Break-even point in units given fixed costs 5,000, price 25, variable cost 15 is which value?
• Ha: μ > 50 implies what type of statistical test?
• Which constraint enforces total production equals 10 tons in the three-product LP?
• What is the annual holding cost per unit for goat cheese?
• An owner must decide whether to move to a new location or renovate. The expected value for moving to a new location is $625,000. Which option best represents this information?
• What is statistical power?
• What is the per-unit production cost of product two?
• Which statement about a perpetuity is true?
• What is the annual cost of purchasing tires (D times price) in the mountain bikes scenario?
• What is the mean of the data set {2, 4, 6, 8, 10}?
• In the LP problem above, the maximum value of 5x + 4y is
• What is the formula for the effective annual rate when interest is compounded m times per year with nominal rate i?
• State the Central Limit Theorem in one sentence.
• Which statement distinguishes correlation from causation?
• In the hospital project network, which activities are the immediate predecessors of J?
• What happens to the mean and variance of the sampling distribution of the sample mean as the sample size grows?
• For a t-test with sample size n = 9, what is the degrees of freedom?
• The IQR equals Q3 - Q1.
• Which expression equals P(X = 3) for X ~ Binomial(n = 10, p = 0.2)?
• With exponential smoothing α = 0.5, F1 = 10, A1 = 12, compute F2.
• Which description best matches a well-specified regression model in terms of residuals?
• An R-squared value of 0.75 indicates what?
• What is the margin of error for the 95% confidence interval for μ given σ = 15 and n = 25?
• What is the probability of a favorable market in this scenario?
• The Poisson distribution can approximate the binomial distribution under certain conditions. Which statement is true?
• Which option is not among the three capacity-expansion alternatives being considered?
• What is a Type II error?
• What is the main objective in this capacity expansion decision?
• How can this employee realistically predict accidents next year?
• In the regression line y = a + b x, what is the slope b if the line is y = 1 + 2x?
• Which is a commonly used method to handle missing data?
• If R^2 = 0.68, what does this say about the model?
• What is multicollinearity?
• Which statement best describes nonnegativity constraints in LP?
• Describe the graphical method to solve a simple linear programming problem with two variables.
• If the right-hand side of the constraint X1 + X2 ≤ 4 is increased by 1, how does the feasible region change?
• In a binomial distribution with n = 5 and p = 0.4, which value is the most likely for X (the mode)?
• In the PERT chart for a project, what is the duration of the critical path?
• If p-value = 0.03 and α = 0.05, should you reject H0?
• In a binomial distribution with n = 5 and p = 0.4, what is P(X = 3)?
• In a hospital renovation project using PERT data, what is the expected completion time for activity A given optimistic 7, most likely 9, pessimistic 14 days?
• Given Y-hat = a + b1 X1 + b2 X2 with a = 3, b1 = 4, b2 = -1, X1 = 3, X2 = 6, what is the predicted value of Y?
• Why are outliers problematic in regression?
• Under a moderate market, which option yields the highest payoff?
• In a multiple regression predicting accidents with independent variables such as number of automobiles registered, sales of alcoholic beverages, and rainfall, which is the dependent variable?
• What VIF value indicates multicollinearity concerns?
• Which of the following is the correct linear programming model for minimizing production cost in the 3-product problem?
• What is the distribution of the sample mean for large n?
• Which statistical test is used to compare a sample mean to a known value when the population standard deviation is unknown?
• Which distribution models the number of successes in a fixed number of trials with constant probability p?
• In the EOQ context for an item with steady demand, which assumption is correct?
• With n = 16, x̄ = 52, s = 6, the 95% CI for μ has a margin of error of 3.20. Which value below represents the margin of error?
• What is the average inventory value for the year?
• Perpetuity value with PMT = 100 and i = 5% is equal to which of the following?
• If the path A-B-E-F-G has a total duration of 17 days, what is the value of E?
• If P(A) = 0.6 and P(B) = 0.5 and A and B are independent, what is P(A and B)?
• The sample standard deviation of the data {2,4,4,4,5,5,7,9} is approximately which value?
• If X ~ Binomial(n=10, p=0.2), what is P(X = 3)?
• In the hospital project network, which activity has immediate predecessors C and F?
• A correlation coefficient of 0.85 indicates which relationship?
• Describe Laspeyres and Paasche index.
• What z-score corresponds to the 90th percentile of the standard normal distribution?
• FV of an ordinary annuity with PMT = 200, i = 5%, n = 10 yields which value?
• Under EOQ in the mountain bikes scenario, what is the annual holding cost component?
• Break-even: FC = 2000, price = 50, VC = 20. Break-even units?
• What is the value of the expression 7^2 / 3^4?
• What is the 3-period moving average forecast for the next period given the last three observations 7, 9, 11?
• In the LP with constraints X1 + X2 ≤ 4 and 2X1 + 5X2 ≤ 10, which constraint is binding at the optimal solution?
• Distinguish the addition rule for probabilities of mutually exclusive events.
• What is the estimated economic order quantity for the goat cheese?
• Which statement best describes the contribution margin (CM) ratio?
• In the LP with Min Z = 26X1 + 14X2 + 12X3 subject to 2X1 + 3X2 + X3 ≥ 30, 6X1 + 3X2 + X3 ≥ 50, X1, X2, X3 ≥ 0, what is the optimal value of X3?
• Relative frequency for 30 occurrences in 150 observations.
• In a 3-period moving average forecast, the forecast for the next period is the average of the previous three observations.
• For a data set with mean 50 and standard deviation 5, what is the coefficient of variation?
• What best describes multicollinearity and its impact in regression analysis?
• Name two sampling methods.
• What is the approximate EOQ (in gallons) for the taxidermist scenario?
• If two events A and B are mutually exclusive, P(A or B) equals which?
• Define a Type I error.
• What is the contribution margin per unit given price 25 and variable cost 15?
• Which of the following is a main linear regression assumption?
• What is the median of the data set 70, 85, 98, 70, 82?
• What is the Pearson correlation coefficient for a perfect positive linear relationship?
• What is the crash time for activity D?
• Larry owns a boutique that makes lamp bases and lampshades. It takes one hour to assemble and wire one lamp base and one hour to assemble and paint one lampshade. Larry works six hours per day and makes identical numbers of bases and shades. What is the constraint?
• What is the probability of being in the youngest or oldest age categories and having a preference for positive hair styling ads?
• What is the purpose of seasonal adjustment in time series analysis?
• With known σ = 15, n = 25, and x̄ = 100, which is the correct 95% confidence interval for μ?
• What is the present value of $1,000 to be received in 3 years at an annual rate of 5%?
• In the first optimal solution of the three-variable LP, what is the value of X1?
• State the Central Limit Theorem in one sentence.
• What is the primary benefit of quantitative analysis when assessing whether revenue has been increasing over the past decade?
• What is the present value of an ordinary annuity of PMT = 100 for n = 3 at i = 5%?
• Which formula defines the effective annual rate (EAR) when the nominal rate is i and compounding m times per year?
• How do you compute the expected monetary value in decision analysis?
• If two events A and B are independent, which statement is true?
• What decision model step is represented by the supplier scoring table that lists On-Time Delivery, Cost, and Capacity with a Total Score?
• In linear programming, which option best defines a feasible solution?
• What is the annual demand for goat cheese in pounds?
• Which ordering frequency minimizes total inventory cost for the taxidermist's resin?
• The data notes a 200% increase in new small businesses licensed to owners aged 18 to 22. This suggests which marketing implication?
• What is true about APR and EAR?
• What is the Net Present Value rule for investment decisions?
• In annuity problems, what does PMT represent?
• If category frequency table A:5, B:12, C:7, D:2, what is the total number of observations?
• Define homoscedasticity.
• What is the multiplication rule for independent events?
• Interpret the regression slope β in y = α + βx.
• What is the total annual inventory cost when EOQ is used in the mountain bikes scenario?
• In linear programming, what does the constraint X1 ≥ 0 signify?
• What is the purpose of a control chart in quality control?
• In a network planning scenario for remodeling a restaurant, what is the expected completion time for activity G?
• Which approach should a marketing manager use to forecast monthly sales with seasonality?
• How do you compute the expected value in a decision tree with probabilities 0.6 and 0.4 and payoffs 100 and -20?
• Which two states of nature are considered in the capacity expansion decision scenario?
• Dawn's kenneling expansion: If she uses the added 1,000 square feet to accommodate larger dogs, the expected annual revenue is $22,000 in a strong economy and $16,000 in a weak economy. If instead she allocates the expansion to dogs under 30 pounds, the revenues are $20,000 (strong) and $17,500 (weak). Which option provides the best expected payout?
• In the goat cheese EOQ problem, what is the unit price used to determine holding costs?
• What is the annual demand for tires in the mountain bikes scenario?
• What is the sample standard deviation of the data set {2, 4, 6, 8, 10}?
• An employee has to decide among four machines; the purchase and installation cost is the same for all. The decision tree indicates that Machine D is optimal. Which machine should be chosen?
• For a Poisson distribution with λ = 4, what is P(X = 2)?
• What is the EOQ value (in tires) given D=2400, S=200, H=24?
• Solve the LP: Maximize 5x + 4y subject to 2x + y ≤ 20, x + 2y ≤ 20, x,y ≥ 0. What are the optimal values and objective?
• For the scenario of moving to the football field with pavilions, which weather condition contributes most to its EV?
• How would a decision tree help Charlie in evaluating whether to expand oven capacity?
• Given a category frequency table A:5, B:12, C:7, D:2 (total 26), identify the mode and relative frequencies.
• What is the additional revenue in a strong economy if expanding to larger dogs?
• In the same LP, what is the optimal value of X2?
• In the Elementary Principles in Finance course, the number of students in five sections are 65, 80, 93, 65, 77. What is the median?
• What is the objective function in the linear program with two decision variables X1 and X2?
• Which of the following expressions correctly represents the present value of a perpetuity paying C per period at rate r?
• If the correlation r = 0.85, what does this indicate about the relationship?
• For X ~ N(μ = 100, σ = 5), what is the z-score for X = 110?
• What does a pattern in residuals suggest in regression?
• Which classification applies to group brainstorming with the nurses and doctors to explore why many patients are coming to the ER for non-emergency treatment?
• Which activity has the highest crash cost in the crashing data?
• Present value of a perpetuity paying C per period at rate r?
• Which statement best describes how skewness affects the mean and median?
• When should you use the t-distribution instead of the z-distribution?
• What is the objective function value for the first optimal solution of the three-variable LP?
• Name a nonparametric alternative to the t-test for comparing two independent means.
• In a capacity-expansion decision scenario, payoffs under a favorable market are Large Plant 13, Small Plant 5, Subcontracting 7; and under a moderate market are 2, 8, 3 respectively. Which option yields the highest payoff in a favorable market?
• For the 500-count copy paper EOQ item, which EOQ assumption is stated as correct?
• What is the present value of 5,000 to be received in 3 years discounted at 10% annually?
• Mutually exclusive events definition.
• Which of the following represents the null and alternative hypotheses for testing whether the population mean equals 50 against a one-sided alternative greater than 50?
• In a regression model, what does the dependent variable represent?
• What is the daily processing time limit in minutes for the plant problem?
• Which classification applies to an open-ended intake question asking why the patient selected this ER?
• In break-even analysis, which statement about fixed costs is true?
• What is the formula for a z-score?
• In the payoffs under a favorable market, which option yields the smallest payoff?
• Regarding lead time in the EOQ model, which statement is correct when lead time does not vary?
• For price 50 and variable cost 20, what is the per-unit contribution margin and its ratio?
• What does seasonality mean in forecasting?
• What is the annual loan payment on a $10,000 loan at 6% for 5 years?
• What is the future value of an ordinary annuity with PMT = 100 for n = 3 at i = 5%?
• Which location yields the second-highest expected value in the craft fair EV table?
• What is the future value of $2,000 invested for 4 years at 6% annual compounding?
• In a positively skewed distribution, which statistic tends to be larger?
• Which statement about multicollinearity is true?
• Define relative frequency.
• What is the probability of rainy weather during the craft fair?
• What is the critical path for the project shown in the PERT chart?
• A fair six-sided die is rolled. What is the probability of obtaining an even number?
• Which statement about a 95% confidence interval for a mean is correct?
• Which method of analysis should this owner use to determine whether to build the recording studio?
• Which index uses base-period quantities?
• What does MAPE stand for?
• Which index uses current-period quantities?
• In a moderate market, which option yields the highest payoff?
• In a boxplot, outliers are defined as values outside which boundaries?
• From a standard deck of 52 cards, what is the probability that two cards drawn without replacement are both aces?
• In ANOVA, the F-statistic is the ratio of which variances?
• Using the regression line y = 1 + 2x, what is the predicted value when x = 4?