90% Confidence Interval for Free Help Line Usage in Businesses

Q1. The Australian Accountant Society conducts a survey to assess whether business use the society’s free help line when completing their quarterly business activity statements. They wanted to know if there is a difference in the proportion of who use the free help line between businesses less than 5 years old (NEW) and businesses 5 years and older (OLD). A random sample was taken. The sample consisted of 400 businesses less than 5 years old (NEW) and 300 businesses 5 years of older (OLD). Forty percent of the new businesses used the free help-line, compared to thirty percent of the old businesses. What is the 90% confidence interval for the true difference in the proportion of who use the free help line between businesses less than 5 years old (NEW) and businesses 5 years and older (OLD)? To calculate the 90% confidence interval for the true difference in the proportion of businesses less than 5 years old (NEW) and businesses 5 years and older (OLD) that use the free help line, you can use the formula for the confidence interval for the difference in two population proportions. The formula is: Confidence Interval=( p ^1− p ^2)± Z ⋅ n 1 p ^1(1− p ^1)+ n 2 p ^2(1− p ^2) Where:  ^1 p ^1 and ^2 p ^2 are the sample proportions of businesses less than 5 years old and businesses 5 years and older, respectively, that use the free help line.  1 n 1 and 2 n 2 are the sample sizes for the two groups.  Z is the Z-score corresponding to the desired confidence level. For a 90% confidence interval, the Z-score is approximately 1.645. Given the information you provided:  ^1 p ^1 (proportion for NEW) = 0.40

 ^2 p ^2 (proportion for OLD) = 0.30  1 n 1 (sample size for NEW) = 400  2 n 2 (sample size for OLD) = 300  Z-score for a 90% confidence interval ≈ 1.645 Now, plug these values into the formula: Confidence Interval=(0.40−0.30)±1.645 ⋅ 0.40(1−0.40)400+0.30(1−0.30)300 Confidence Interval=(0.40−0.30)±1.645 ⋅ 4000.40(1−0.40)+3000.30(1−0.30) Calculate the values inside the square root first: 0.40(0.60)400+0.30(0.70)3004000.40(0.60)+3000.30(0.70) Now, calculate the square root: 0.24400+0.213004000.24+3000.21 Next, calculate the values inside the square root: 0.0006+0.00070.0006+0.0007 Now, calculate the square root: 0.0013≈0.036060.0013=0.03606 Now, plug this value back into the confidence interval formula: Confidence Interval=(0.10)±1.645 ⋅ 0.03606 Confidence Interval=(0.10)±1.645 ⋅ 0.03606 Calculate the range: Confidence Interval=0.10±0.05942 Confidence Interval=0.10±0.05942 Now, calculate the upper and lower limits of the confidence interval:

Upper Limit = 0.10 + 0.05942 = 0.15942 Lower Limit = 0.10 - 0.05942 = 0.04058 So, the 90% confidence interval for the true difference in the proportion of businesses that use the free help line between businesses less than 5 years old (NEW) and businesses 5 years and older (OLD) is approximately (0.0406, 0.1594). Q2. A business has sales of $295 000, purchases of $225 000, a beginning inventory of $150 000 and an ending inventory of $118 000. Calculate gross profit. Gross profit can be calculated using the following formula: Gross Profit=Sales−Cost of Goods Sold (COGS) To calculate COGS, you can use the following formula: COGS=Beginning Inventory+Purchases−Ending Inventory Given the information you provided:  Sales = $295,000  Purchases = $225,000  Beginning Inventory = $150,000  Ending Inventory = $118,000 First, calculate COGS: COGS = $150,000 + $225,000 - $118,000 Now, calculate COGS:

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COGS = $375,000 - $118,000 = $257,000 Now that you have the value of COGS, you can calculate the gross profit: Gross Profit = $295,000 - $257,000 = $38,000 So, the gross profit is $38,000. Q3. Calculator Pty Ltd has a beginning balance of equity of $82 000; an ending balance of $37 000; and a loss for the period of $33 000. Calculate how much the owner of Calculator Pty Ltd withdrew during the period for personal use. To calculate how much the owner of Calculator Pty Ltd withdrew during the period for personal use, you can use the following formula: Owner's Withdrawals = Beginning Equity + Net Income - Ending Equity Where:  Beginning Equity is the starting balance of equity.  Net Income is the profit or loss for the period.  Ending Equity is the ending balance of equity. Given the information you provided  Beginning Equity = $82,000  Net Loss = $33,000 (negative because it's a loss)  Ending Equity = $37,000 Now, plug these values into the formula

Owner's Withdrawals = $82,000 - $33,000 - $37,000 Now, calculate Owner's Withdrawals = $82,000 - $33,000 - $37,000 = $82,000 - $70,000 = $12,000 So, the owner of Calculator Pty Ltd withdrew $12,000 during the period for personal use. Q4. If sales revenue is $600 000 and cost of sales is $450 000, what is the gross profit margin? The gross profit margin is calculated as a percentage of gross profit relative to sales revenue. The formula for calculating the gross profit margin is Gross Profit Margin=(Gross ProfitSales Revenue)×100% Given the information provided  Sales Revenue = $600,000  Cost of Sales (COGS) = $450,000 First, calculate the Gross Profit Gross Profit = Sales Revenue - Cost of Sales (COGS) = $600,000 - $450,000 = $150,000 Now, plug this value into the formula for Gross Profit Margin Gross Profit Margin = \left( \frac{$150,000}{$600,000} \right) * 100\% Now, calculate the Gross Profit Margin Gross Profit Margin=(14)×100% =25%

So, the gross profit margin is 25%. This means that for every dollar of sales revenue, the company retains 25 cents as gross profit after accounting for the cost of sales. Q5. Which one of the following is an example of other comprehensive income? a. Dividends received b. Sales income c. Revaluations of assets recorded in the revaluation surplus account d. Royalties The correct answer is c. Revaluations of assets recorded in the revaluation surplus account Other comprehensive income (OCI) includes items of income and expense that are not recognized in the income statement (profit and loss) but are instead recognized directly in equity. One common example of OCI is revaluations of assets, such as property, plant, and equipment, recorded in the revaluation surplus account. These revaluations can lead to changes in the carrying amount of assets and are reported in the comprehensive income statement as part of OCI. Q6. For the financial year ending 30 June, Daily Ltd had a beginning balance for equity of $180 000 and an ending balance of $175 000. During the year, the owner withdrew $120 000 for private use. How much profit did Daily Ltd earn during the year? To determine the profit earned by Daily Ltd during the year, you can use the following formula

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Profit = Ending Equity + Owner's Withdrawals - Beginning Equity Where  Beginning Equity is the starting balance of equity.  Ending Equity is the ending balance of equity.  Owner's Withdrawals are the withdrawals made by the owner during the year. Given the information you provided  Beginning Equity = $180,000  Ending Equity = $175,000  Owner's Withdrawals = $120,000 Now, plug these values into the formula Profit = $175,000 + $120,000 - $180,000 Now, calculate the profit Profit = $295,000 - $180,000 = $115,000 So, Daily Ltd earned a profit of $115,000 during the year. Q7. Which of the following is not disclosed in the statement of comprehensive income? a. Income and expenses recognised directly in equity b. Transactions with owners c. transactions not recognised in the statement of profit or loss d. Income and expenses recognised in the statement of profit or loss d. Income and expenses recognised in the statement of profit or loss

The statement of comprehensive income typically includes income and expenses recognized in the statement of profit or loss, as well as income and expenses recognized directly in equity. Therefore, option (d) is the one that is not disclosed in the statement of comprehensive income. Q8. If profit after tax and interest is $400 000, interest expense is $50 000 and taxation expense is $84 000, what is profit before interest and tax? To find the profit before interest and tax, you can use the following formula Profit Before Interest and Tax = Profit After Tax and Interest + Interest Expense + Taxation Expense Given the information you provided  Profit After Tax and Interest = $400,000  Interest Expense = $50,000  Taxation Expense = $84,000 Now, plug these values into the formula Profit Before Interest and Tax = $400,000 + $50,000 + $84,000 Now, calculate the profit before interest and tax Profit Before Interest and Tax = $534,000 So, the profit before interest and tax is $534,000. Q9. For a retailing or manufacturing company, gross profit is equal to sales revenue less __________. a. all expenses

b. inventory c. purchases d. Cost of sales d. Cost of sales Gross profit for a retailing or manufacturing company is calculated as sales revenue minus the cost of sales (also known as cost of goods sold or COGS). Therefore, the correct option is (d) "Cost of sales." Q10. For the financial year ending 30 June, Kim's Mowing had a beginning balance for equity of $64,000 and an ending balance of $124,000. During the year, the owner withdrew $50,000 for private use. How much profit did Kim's Mowing earn during the year? To determine the profit earned by Kim's Mowing during the year, you can use the following formula Profit=Ending Equity+Owner’s Withdrawals−Beginning Equity Where:  Beginning Equity is the starting balance of equity.  Ending Equity is the ending balance of equity.  Owner's Withdrawals are the withdrawals made by the owner during the year. Given the information provided:  Beginning Equity = $64,000  Ending Equity = $124,000

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 Owner's Withdrawals = $50,000 Now, plug these values into the formula: Profit = $124,000 + $50,000 - $64,000 Now, calculate the profit: Profit = $174,000 - $64,000 = $110,000 So, Kim's Mowing earned a profit of $110,000 during the year. Q11. A business has sales of $455 000, purchases of $225 000, a beginning inventory of $150 000 and an ending inventory of $118 000. Calculate gross profit. To calculate gross profit, you can use the following formula: Gross Profit = Sales - Cost of Goods Sold (COGS) To calculate COGS, you can use the following formula: COGS = Beginning Inventory + Purchases - Ending Inventory Given the information you provided:  Sales = $455,000  Purchases = $225,000  Beginning Inventory = $150,000  Ending Inventory = $118,000 Now, let's calculate COGS: COGS = $150,000 + $225,000 - $118,000 COGS = $375,000 - $118,000 COGS = $257,000

Now that you have the value of COGS, you can calculate the gross profit: Gross Profit = Sales - COGS Gross Profit = $455,000 - $257,000 Gross Profit = $198,000 So, the gross profit is $198,000.

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