Business Statistics and Financial Accounting, Review of Statistical and Accounting Concepts @AccAnalyticsCPA ​

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 Review of Statistical and Accounting Concepts

1. Introduction

This document provides a review of key concepts from introductory business statistics and financial accounting, as presented in the provided source materials. The focus is on summarizing core ideas, statistical methods, and accounting principles that are foundational to business analysis and decision-making.

2. Key Statistical Concepts and Methods

• Student's t-Distribution: The t-distribution is crucial when dealing with sample data, especially when the population standard deviation is unknown.
• Key Idea: The t-table (Table 2.2 in the "Introductory-Business-Statistics-with-Interactive-Spreadsheets" document) provides probabilities for exceeding a given t-score, with degrees of freedom (df) influencing the distribution. For example:
• "With 5 df, there is a .05 probability that a sample will have a t-score > 2.015."
• Skewness: Skewness describes the asymmetry of a distribution.
• Key Ideas:A normal distribution has a skewness of zero.
• Negative skewness indicates a left-skewed distribution (longer tail on the left).
• Positive skewness indicates a right-skewed distribution (longer tail on the right).
• "The skewness characterizes the degree of asymmetry of a distribution around its mean."
• "A positive value of skewness signifies a distribution with an asymmetric tail extending out towards more positive X and a negative value signifies a distribution whose tail extends out towards more negative X."
• Descriptive Statistics and Data Organization: The sources demonstrate the importance of organizing and summarizing data.
• Key Ideas:Calculating and interpreting quartiles, percentiles, and medians.
• Creating line graphs and stemplots for data visualization.
• Example: Exercises include finding quartiles and percentiles from a data set about the weights of San Francisco 49ers players.
• Probability Distributions: Understanding various distributions is essential for statistical analysis.
• Key Ideas:Uniform Distribution: Defined by a constant probability within a range (a, b). Formulas for mean, standard deviation, and probabilities are provided.
• For a random variable X that follows a uniform distribution between a and b (X ~ U (a, b)):
• The mean is calculated as (a+b)/2
• The standard deviation is sqrt[(b-a)^2/12]
• Probability density function for x = 1 / (b-a)
• Area to the Left of x: P(X < x) = (x – a) / (b - a)
• Area to the Right of x: P(X > x) = (b – x) / (b - a)
• Area Between c and d: P(c < x < d) = (d – c) / (b-a)
• Normal Distribution: Described by its mean (μ) and standard deviation (σ).
• Standard Normal Distribution: A special case where μ = 0 and σ = 1, represented as Z ~ N(0, 1).
• Z-scores are used to standardize values. The formula for converting a value x to a z-score is: z = (x – μ) / σ. Also, the formula for converting a z-score to an observed value, x is: x = μ + (z)σ
• Hypothesis Testing: Tests are conducted to make claims about a population based on sample data.
• Key Ideas:Null hypothesis (H0) and alternative hypothesis (Ha).
• Left-tailed, right-tailed, and two-tailed tests. Examples of setting up null and alternate hypotheses are:
• H0: μ = 34; Ha: μ ≠ 34
• H0: p ≤ 0.60; Ha: p > 0.60
• H0: μ ≥ 100,000; Ha: μ < 100,000
• The document features an example of testing for a difference in weighted alphas between bank stocks in the northeast and west regions using a 5% significance level.
• Confidence Intervals: Used to estimate population parameters based on sample data with a certain level of confidence. The document indicates this is used to examine the average number of M&Ms in a bag.
• F-Distribution: Used in Analysis of Variance (ANOVA) testing.
• The document mentions MSbetween and MSwithin which are variances between and within groups respectively and discusses calculating sum of squares. It provides an example of using an F-test to test equality between means across 5 groups.
• The formula for the F-statistic is: F = (MSbetween) / (MSwithin)
• Degrees of freedom are calculated for both the numerator (df(num)) and denominator (df(denom))
• df(num) = k – 1 where k is the number of different groups
• df(denom) = n – k where n is the total number of all values combined
• Z-Score and Probability Calculations
• The sources provide examples of calculations for z-scores: z = -2, z=2, z=2.78, z=-1.67, z ≈ -0.33
• It also provides examples of finding values based on z-scores: x=20, x=6.5, x=1, x=1.97
• It provides examples of finding areas under a normal curve. For example, about 68% of values are within 1 standard deviation of the mean, about 4% of values are more than 2 standard deviations from the mean. Other examples given are about 50% of values fall below the mean and about 27% of values fall between 1 and 2 standard deviations below the mean.
• It explains that for a continuous probability distribution, P(x=1) = 0.

3. Key Financial Accounting Principles and Practices

• Core Concepts:
• Accounting Defined: The process of identifying, measuring, and communicating economic information.
• Business Organizations: Includes proprietorships, partnerships, and corporations.
• Generally Accepted Accounting Principles (GAAP): A common set of accounting principles, standards, and procedures that companies must follow when they compile their financial statements.
• Financial Statements: The balance sheet, income statement, and statement of cash flows.
• Accounting Process:
• Accounts: Tracking increases and decreases in assets, liabilities, and equity.
• Transaction Analysis: Understanding the impact of business events on the accounting equation (Assets = Liabilities + Equity).
• Double-Entry Accounting: Each transaction affects at least two accounts.
• Trial Balance: A list of all accounts with their balances used to verify the equality of debits and credits.
• Accounting Cycle: The steps involved in processing transactions from start to finish.
• Adjusting Entries: Made at the end of the accounting period to allocate revenues and expenses to the appropriate periods (including accrued revenues/expenses, prepaid expenses, depreciation and unearned revenue).
• Specific Accounting Topics:
• The Operating Cycle: The time it takes a company to purchase inventory, sell it, and collect cash from the sale.
• Classified Balance Sheet: Distinguishes between current and non-current assets and liabilities.
• Notes to Financial Statements: Provide additional detail and explanations.
• Auditor's Report: An independent assessment of financial statements.
• Management's Responsibility: Management is responsible for financial statement preparation.
• Merchandising Transactions: Includes the purchase, sale, and adjustment of merchandise inventory. Transactions involving the perpetual inventory system are described. The document describes the difference between the perpetual and periodic inventory systems.
• "When goods are purchased using the periodic inventory system, the cost of merchandise is recorded in a Purchases account in the general ledger, rather than in the Merchandise Inventory account as is done under the perpetual inventory system."
• Inventory Cost Flow Assumptions: LIFO, FIFO, and weighted-average methods for assigning costs to inventory.
• Petty Cash: A small amount of cash on hand for minor expenses. Examples are given of reimbursement entries.
• Internal Control: Procedures designed to safeguard assets and ensure accurate accounting.
• Accounts Receivable: Money owed to the company by customers; includes recording sales, returns, bad debts, and recoveries.
• Short-Term Notes Receivable: Promissory notes with a maturity of less than one year.
• Long-Lived Assets: Property, plant, and equipment (PPE), depreciation, amortization, impairments, and disposal.
• Examples of journal entries to record purchasing land and building for a lump sum, depreciation expense, trade-in and sale of old equipment and purchase of a patent (intangible asset) are given.
• Debt Financing: Current and long-term liabilities, bonds payable, and loans payable. Examples are given of journal entries related to issuing bonds, paying interest on bonds, and redeeming bonds.
• The difference between the face value of the bond ($1,000) and the selling price of the bond ($991) is $9. This is the discount.*
• Example entries to record blended principal and interest payments are also provided.
• Sales Taxes: GST, PST, QST, and HST.
• Equity Financing: Common and preferred shares, cash dividends, and share dividends. Examples are provided of journal entries to record share issuances and share dividends.
• "The market price on the date of declaration is used to record a share dividend."
• Statement of Cash Flows: Tracks the movement of cash into and out of a business, broken down into operating, investing and financing activities.
• Financial Statement Analysis: Uses ratio analysis to assess a company's financial health. Liquidity, profitability, leverage and market ratios are identified as key metrics to analyze. Horizontal and vertical trend analysis are also discussed.
• Proprietorships and Partnerships: Accounting for these types of businesses, including capital accounts and profit/loss allocation. Examples are given of journal entries to record partner investment in the business, withdrawals, and profit allocations based on fractional allocation.
• Journal Entries: The document provides numerous examples of journal entries to record various transactions. These include (but are not limited to):
• Cash disbursements journal
• Bank reconciliations and service charges
• The purchase of merchandise inventory under perpetual and periodic systems
• Sale of merchandise and cost of goods sold
• Purchase discounts
• Sales returns and allowances
• Adjustments for shrinkage of inventory
• Reimbursing petty cash funds
• Credit card fees
• Bad debts
• Issuance of bonds at premium or discount
• Paying interest on debt
• Redemption of bonds
• Issuance of common and preferred stock
• Declaration of cash and stock dividends
• Recording partner's investments and withdrawals
• Allocating income to partners

4. Conclusion

These sources provide a comprehensive overview of foundational concepts in business statistics and financial accounting. They emphasize the importance of understanding data analysis, statistical inference, and the principles of financial reporting. The materials include numerical examples and detailed explanations of how statistical and accounting techniques are applied in a business context, including example entries in the general journal. These concepts are critical for effective business decision-making and financial analysis.