Data analysis and statistical techniques

A public utility company wants to survey its customers regarding a new pricing structure. The customer base is divided into three distinct income brackets: Low, Medium, and High. The company wants to ensure that the sample reflects the exact proportion of each income bracket in the total customer base, and then selects customers randomly within those brackets. Which sampling method is being used?

A logistics company recorded the following maintenance costs and activity levels over the last four months: Month 1: 12,000 miles, $45,000 Month 2: 15,000 miles, $51,000 Month 3: 10,000 miles, $41,000 Month 4: 18,000 miles, $57,000 Using the high-low method, calculate the variable maintenance cost per mile. (Enter the number only, to two decimal places, e.g., 1.50)

A construction firm uses a Laspeyres price index to monitor the cost of building materials. Base year (2020) prices and quantities were: Cement: $10/bag, 500 bags Steel: $50/ton, 100 tons Current year (2023) prices are: Cement: $12/bag Steel: $60/ton What is the Laspeyres price index for 2023 (base year 2020 = 100)?

A seasonal ski resort uses time series analysis to forecast visitor numbers. The trend equation is Y = 5,000 + 200Q, where Q is the quarter number (Q1 2020 = 1). The resort uses a multiplicative model. The seasonal variation for Quarter 1 is +20% (or 1.20). What is the forecasted number of visitors for Quarter 1 of 2022 (which is Q = 9)?

A biotech firm is developing a new drug. There is a 40% probability that the drug will be highly successful, yielding a profit of $10 million. There is a 50% probability of moderate success, yielding $2 million. There is a 10% probability of failure, resulting in a loss of $5 million. What is the expected value of the profit from this drug development?

A data analyst calculates the correlation coefficient (r) between advertising spend and sales revenue to be 0.80. What does the coefficient of determination indicate in this context?

A manufacturing process produces steel bolts. The length of the bolts is normally distributed with a mean of 100 mm and a standard deviation of 2 mm. What is the Z-score for a bolt that measures 105 mm?

Section A MetroWater, a public utility company, uses sampling to test water quality. An automated system selects every 50th water sample passing through the main filtration valve for detailed chemical analysis. Which sampling method is being utilized?

A cross-border logistics company uses an additive time series model to forecast shipping volumes. The trend equation is T = 5,000 + 200Q (where Q is the quarter number, starting with Q=1 for Q1 20X1). The seasonal variation for Quarter 3 is +450. What is the forecast for shipping volumes in Quarter 3 of 20X2 (Q=7)?

A heavy manufacturing firm tracks the cost of two key raw materials. Base Year (Year 0): Material A price $10, quantity 100. Material B price $20, quantity 50. Current Year (Year 1): Material A price $12, quantity 110. Material B price $25, quantity 60. Calculate the Laspeyres price index for Year 1 (Base Year = 100). Enter your answer to one decimal place.

A market research service firm is conducting a survey on consumer habits. They divide the population into distinct age groups and then randomly select individuals from each group in proportion to the group's size in the overall population. Which TWO statements about this sampling method are correct?

A tech company calculates the correlation coefficient (r) between its monthly marketing spend and its monthly software subscriptions to be +0.85. Which of the following statements is the most accurate interpretation of this result?

An agricultural firm is deciding whether to plant a new crop. The potential profits depend on weather conditions: - Good weather (30% probability): $100,000 profit - Average weather (50% probability): $150,000 profit - Poor weather (20% probability): $80,000 profit Calculate the expected value of the profit. (Enter numbers only)

A public utility company monitors the daily electricity consumption of a city. The consumption follows a normal distribution with a mean of 500 MW and a standard deviation of 20 MW. Approximately what percentage of days will have a consumption between 460 MW and 540 MW?

**Section A** TitaniumForge operates a heavy steel forging plant. The total electricity costs recorded at two different activity levels are as follows: - Highest activity: 15,000 machine hours, Total Cost: $85,000 - Lowest activity: 8,000 machine hours, Total Cost: $57,000 Using the high-low method, calculate the estimated total electricity cost for an activity level of 12,000 machine hours. *(Enter your answer as a whole number without the dollar sign or commas)*

**Section A** Oceanic Freight, a cross-border shipping multinational, uses index numbers to analyze its fuel costs over the last decade. What is the primary purpose of using index numbers in this context?

**Section A** A tech company analyzes its daily server load using a 7-day moving average. What is the main statistical reason for applying a moving average to this time series data?

**Section A** An agricultural cooperative calculates the correlation coefficient (r) between annual rainfall and crop yield to be +0.92. How should this result be interpreted?

**Section A** HopeFoundation, an NGO, is planning a fundraising campaign. The management accountant has estimated the following probabilities for the net funds raised: - 30% probability of raising $50,000 - 50% probability of raising $30,000 - 20% probability of raising $10,000 Calculate the Expected Value (EV) of the funds raised. *(Enter your answer as a whole number without the dollar sign or commas)*

**Section A** A service firm wants to survey its clients. The client base consists of 60% small businesses, 30% medium enterprises, and 10% large corporations. The researcher selects a sample that exactly matches these proportions. Which sampling method has been used?