Statistical Inference: Hypothesis Testing and Confidence Intervals
Chapter 17: Inferences When Standard Deviation is Unknown
Big Idea: T-Test for Unknown Standard Deviation
The t-test is used when the population standard deviation (SD) is unknown. It has fewer conditions than z-tests for inferences about a mean:
- Data is a simple random sample (SRS) from a larger population.
- Observations follow a normal distribution.
- We estimate standard error using s / √n, where s is the sample SD and √n accounts for the variability of sample means.
T-Test Formula and Properties
The
Read MoreLinear Programming Problems and Solutions
Problem #B-1: Simultaneous Equations for Optimization
a. Maximize Z = 4×1 + 3×2
Subject to:
Material: 6×1 + 4×2 <= 48 lb (x1 = 2)
Labor: 4×1 + 8×2 <= 80 hr (x2 = 9)
x1, x2 >= 0 (Profit = 35)
b. Maximize Z = 6A + 3B
Subject to:
Material: 20A + 6B <= 600 lb (A = 24)
Machinery: 25A + 20B <= 1000 hr (B = 20)
A, B >= 0 (Profit = 204)
Problem #B-2: Microwave Oven Production
An appliance manufacturer produces two models of microwave ovens: H and W. The goal is to determine the quantities of H and
Read MoreInventory Management and Economic Order Quantity (EOQ) Analysis
Problem #12-1: ABC Inventory Analysis for the Welsh Corporation
The Welsh Corporation utilizes 10 key components in one of its manufacturing plants. The task is to perform an ABC analysis based on the provided data and explain the rationale behind the classification.
Data and Calculations
| SKU | Item Cost ($) | Annual Demand |
|---|---|---|
| WC219 | 0.10 | 12,000 |
| WC008 | 1.20 | 22,500 |
| WC916 | 3.20 | 700 |
| WC887 | 0.41 | 6,200 |
| WC397 | 5.00 | 17,300 |
| WC654 | 2.10 | 350 |
| WC007 | 0.90 | 225 |
| WC419 | 0.45 | 8,500 |
| WC971 | 7.50 | 2,950 |
| WC713 | 10.50 | 1,000 |
ABC Classification and Explanation
Based on the
Read MoreMultivariate Analysis of Variance (MANOVA)
MANOVA
NOTES
Using DVs in combination through MANOVA circumvents this high experimentwise error rate. Then ANOVA is used to identifymain source of these effects. Researcher is mainly interested inresults ofANOVA
MANOVA combines DVs in diff ways so as to maximizeseparation ofconditions specified by each comparison indesign. – designs including a within-subjects factor having more than 2 levels must meetsphericity assumption. However,most common within-subject factor in applied research is time
Read MoreTax Implications of Investment Property Ownership and Retirement Planning
REVISION QUESTIONS SELECTION
QUESTION 1
Jason, a 32-year-old physiotherapist earning $65,000 annually, seeks advice on purchasing an investment property for $400,000 with a $280,000 loan. He plans to reside in the property after six years. He has $120,000 in shares (current value $130,000, cost base $80,000) and anticipates the following property income and expenses:
Estimated Rental Income: $20,000
Estimated Expenses:
- Rates: $2,000
- Insurance: $600
- Loan Interest: $25,400
- Depreciation (fixtures and fittings)
Inventory Management: Costing Methods & Journal Entries
Perpetual Inventory System
The perpetual inventory system continuously updates inventory records to reflect purchases, sales, and returns.
Inventory Costing Methods
Gross Profit Method
Estimates the cost of goods sold based on the gross profit percentage and net sales.
Specific Identification
Tracks the cost of each individual item sold and remaining in inventory.
Weighted-Average Method
Calculates the average cost per unit and applies it to both cost of goods sold and ending inventory.