Kaelea, Inc., has no
debt outstanding and a total market value of $100,000. Earnings
before interest and taxes, EBIT, are projected to be $8,400 if
economic conditions are normal. If there is strong expansion in the
economy, then EBIT will be 24 percent higher. If there is a
recession, then EBIT will be 31 percent lower. The company is
considering a $35,000 debt issue with an interest rate of 6
percent. The proceeds will be used to repurchase shares of stock.
There are currently 4,000 shares outstanding. Assume the company
has a market-to-book ratio of 1.0.
a. Calculate return on equity, ROE, under each of
the three economic scenarios before any debt is issued, assuming no
taxes. (Do not round intermediate calculations and enter
your answers as a percent rounded to 2 decimal places, e.g.,
32.16.)
| ROE | |
| Recession | % |
| Normal | % |
| Expansion | % |
b. Calculate the percentage changes in ROE when
the economy expands or enters a recession, assuming no taxes.
(A negative answer should be indicated by a
minussign. Do not round intermediate calculations
and enter your answers as a percent rounded to the nearest whole
number, e.g., 32.)
| %ΔROE | |
| Recession | % |
| Expansion | % |
Assume the firm goes through with the proposed recapitalization and
no taxes.
c. Calculate return on equity, ROE, under each of
the three economic scenarios after the recapitalization.
(Do not round intermediate calculations and enter your
answers as a percent rounded to 2 decimal places, e.g.,
32.16.)
| ROE | |
| Recession | % |
| Normal | % |
| Expansion | % |
d. Calculate the percentage changes in ROE for
economic expansion and recession. (A negative answer should
be indicated by a minus sign. Do not round
intermediate calculations and enter your answers as a percent
rounded to 2 decimal places, e.g.,
32.16.)
| %ΔROE | |
| Recession | % |
| Expansion | % |
Assume the firm has a tax rate of 35 percent.
e. Calculate return on equity, ROE, under each of
the three economic scenarios before any debt is issued. Also,
calculate the percentage changes in ROE for economic expansion and
recession. (A negative answer should be indicated by a
minus sign. Do not round intermediate calculations
and enter your answers as a percent rounded to 2 decimal places,
e.g., 32.16.)
| ROE | |
| Recession | % |
| Normal | % |
| Expansion | % |
| %ΔROE | |
| Recession | % |
| Expansion | % |
f. Calculate return on equity, ROE, under each of
the three economic scenarios after the recapitalization. Also,
calculate the percentage changes in ROE for economic expansion and
recession, assuming the firm goes through with the proposed
recapitalization. (A negative answer should be indicated by
a minus sign. Do not round intermediate
calculations and enter your answers as a percent rounded to 2
decimal places, e.g.,
32.16.)
| ROE | |
| Recession | % |
| Normal | % |
| Expansion | % |
| %ΔROE | |
| Recession | % |
| Expansion | % |
In: Finance
ABC CORPORATION
Balance Sheet
Year Ended December 31 (in $ millions)
|
Assets |
2006 |
2005 |
Liabilities & Stockowner’s Equity |
2006 |
2005 |
|
|
Current Assets |
Current Liabilities |
|||||
|
Cash |
22.2 |
19.5 |
Accounts Payable |
39.2 |
24.5 |
|
|
Accounts Receivables |
18.5 |
13.2 |
Notes Payable / Short-Term Debt |
4.5 |
3.2 |
|
|
Inventories |
27.2 |
14.3 |
Current Maturities of Long-Term Debt |
13.3 |
12.3 |
|
|
Other Current Assets |
2.0 |
1.0 |
Other Current Liabilities |
8.0 |
4.0 |
|
|
Total Current Assets |
69.9 |
48.0 |
Total Current Liabilities |
65.0 |
45.0 |
|
|
Long Term Assets |
Long-Term Liabilities |
|||||
|
Land |
22.2 |
20.7 |
Long-Term Debt |
98.9 |
56.3 |
|
|
Buildings |
46.5 |
30.5 |
Capital Lease Obligations |
--- |
--- |
|
|
Equipment |
39.7 |
33.2 |
Total Debt |
98.9 |
56.3 |
|
|
Less Accumulated Depreciation |
(18.7) |
(17.5) |
Deferred Taxes |
15.6 |
7.4 |
|
|
Net Property, Plant, and Equipment |
89.7 |
66.9 |
Other Long-Term Liabilities |
---- |
---- |
|
|
Goodwill |
22.0 |
--- |
Total Long Term Liabilities |
114.5 |
63.7 |
|
|
Other Long-Term Assets |
41.0 |
14.0 |
Total Liabilities |
179.5 |
108.7 |
|
|
Total Long Term Assets |
152.7 |
80.9 |
Stockholder’s Equity |
43.1 |
20.2 |
|
|
Total Assets |
222.6 |
128.9 |
Total Liabilities and Stockholder’s Equity |
222.6 |
128.9 |
ABC Corporation
Income Statement
Year Ended December 31 ($ in millions)
|
2006 |
2005 |
|
|
Total Sales |
198.8 |
176.1 |
|
Cost of Sales |
(153.4) |
(147.3) |
|
Gross Profit |
35.4 |
28.8 |
|
Selling, General and Administration Expenses |
(13.5) |
(13.0) |
|
Research and Development |
(9.2) |
(7.6) |
|
Depreciation and Amortization |
(6.2) |
(1.1) |
|
Operating Income |
16.5 |
7.1 |
|
Other Income |
---- |
---- |
|
Earnings Before Interest and Tax (EBIT) |
16.5 |
7.1 |
|
Interest Income (or Expense) |
(7.7) |
(4.6) |
|
Pretax Income |
8.8 |
2.5 |
|
Taxes |
(0.7) |
(0.6) |
|
Net Income |
8.1 |
1.9 |
|
Earnings per share |
$0.556 |
$0.528 |
|
Diluted Earnings Per Share |
$0.526 |
$0.500 |
ABC Corporation has 5.8 million shares outstanding and shares are trading for $20
Calculate the following for 2006:
Quick Ratio
Current Ratio
Market to Book Ratio
Debt to Equity Ratio
Enterprise Value
EPS
Operating Margin
Net Profit Margin
Return on Equity
P/E Ratio
Inventory Turnover
Days of Sales Outstanding
ROA
ROE
Did the tax rate increase from 2005 to 2006? If so, by how much?
In: Finance
You have just been hired as a financial analyst for Lydex Company, a manufacturer of safety helmets. Your boss has asked you to perform a comprehensive analysis of the company’s financial statements, including comparing Lydex’s performance to its major competitors. The company’s financial statements for the last two years are as follows: Lydex Company Comparative Balance Sheet This Year Last Year Assets Current assets: Cash $ 880,000 $ 1,120,000 Marketable securities 0 300,000 Accounts receivable, net 2,380,000 1,480,000 Inventory 3,520,000 2,200,000 Prepaid expenses 240,000 180,000 Total current assets 7,020,000 5,280,000 Plant and equipment, net 9,360,000 8,970,000 Total assets $ 16,380,000 $ 14,250,000 Liabilities and Stockholders' Equity Liabilities: Current liabilities $ 3,930,000 $ 2,820,000 Note payable, 10% 3,620,000 3,020,000 Total liabilities 7,550,000 5,840,000 Stockholders' equity: Common stock, $75 par value 7,500,000 7,500,000 Retained earnings 1,330,000 910,000 Total stockholders' equity 8,830,000 8,410,000 Total liabilities and stockholders' equity $ 16,380,000 $ 14,250,000 Lydex Company Comparative Income Statement and Reconciliation This Year Last Year Sales (all on account) $ 15,780,000 $ 12,780,000 Cost of goods sold 12,624,000 9,585,000 Gross margin 3,156,000 3,195,000 Selling and administrative expenses 1,794,000 1,572,000 Net operating income 1,362,000 1,623,000 Interest expense 362,000 302,000 Net income before taxes 1,000,000 1,321,000 Income taxes (30%) 300,000 396,300 Net income 700,000 924,700 Common dividends 280,000 462,350 Net income retained 420,000 462,350 Beginning retained earnings 910,000 447,650 Ending retained earnings $ 1,330,000 $ 910,000 To begin your assignment you gather the following financial data and ratios that are typical of companies in Lydex Company’s industry: Current ratio 2.3 Acid-test ratio 1.0 Average collection period 30 days Average sale period 60 days Return on assets 8.4 % Debt-to-equity ratio 0.7 Times interest earned ratio 5.7 Price-earnings ratio 10 2. You decide next to assess the company’s stock market performance. Assume that Lydex’s stock price at the end of this year is $78 per share and that at the end of last year it was $46. For both this year and last year, compute: (Round your "Percentage" answers to 1 decimal place and other intermediate and final answers to 2 decimal places.) a. The earnings per share. b. The dividend yield ratio. c. The dividend payout ratio. d. The price-earnings ratio. e. The book value per share of common stock.
In: Accounting
| Ages | Number of students |
|---|---|
| 15-18 | 5 |
| 19-22 | 6 |
| 23-26 | 3 |
| 27-30 | 9 |
| 31-34 | 9 |
| 35-38 | 6 |
Find the relative frequency for the class with lower class limit
19
Relative Frequency = %
Give your answer as a percent, rounded to two decimal places
A Frequency Distribution Table using data
This list of 16 random numbers has been sorted:
| 22 |
| 29 |
| 34 |
| 34 |
| 35 |
| 40 |
| 43 |
| 50 |
| 50 |
| 50 |
| 51 |
| 53 |
| 54 |
| 55 |
| 56 |
| 56 |
Fill in this table with the frequencies as whole numbers and the relative frequencies as decimals with 4 decimal places for the relative frequencies. Remember: relative frequencies are between 0.0 and 1.0
(This problem does not accept fractions.)
| Class | Frequency | Rel.Freq |
| 20-29 | ||
| 30-39 | ||
| 40-49 | ||
| 50-59 |
Complete the table.
| Ages | Number of students | Cumulative Frequency |
|---|---|---|
| 15-18 | 3 | |
| 19-22 | 3 | |
| 23-26 | 4 | |
| 27-30 | 2 | |
| 31-34 | 8 | |
| 35-38 | 2 |
In a student survey, fifty-two part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:
Please round your answer to 4 decimal places for the Relative Frequency if possible.
| # of Courses | Frequency | Relative Frequency | Cumulative Frequency |
| 1 | 18 | ||
| 2 | 0.3077 | 34 | |
| 3 | 18 | 0.3462 | 52 |
What percent of students take exactly one courses? %
50 part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:
| # of Courses | Frequency | Relative Frequency | Cumulative Frequency |
| 1 | 13 | 0.26 | |
| 2 | 24 | ||
| 3 |
a. Complete the table.
b. What percent of students take exactly two courses? %
70 adults with gum disease were asked the number of times per week they used to floss before their diagnoses. The (incomplete) results are shown below:
| # of times floss per week | Frequency | Relative Frequency | Cumulative Frequency |
| 0 | 0.1 | 7 | |
| 1 | 10 | 0.1429 | 17 |
| 2 | 4 | 0.0571 | 21 |
| 3 | 9 | 30 | |
| 4 | 11 | 0.1571 | |
| 5 | 9 | 0.1286 | 50 |
| 6 | 13 | 0.1857 | 63 |
| 7 | 7 | 0.1 | 70 |
a. Complete the table (Use 4 decimal places when applicable)
b. What is the cumulative relative frequency for flossing 1 time per week? %
In: Statistics and Probability
Susan is a 67-year-old white female who works part-time at the library and volunteers at least 10 hours per week. She and her husband live in a two-story home; her children and grandchildren visit every 6 months. She and her husband travel at least twice per year. She participates in water aerobics and yoga 4 days per week for 1 hour each. She will eat lunch at casual dining restaurants at least four times per week. She consumes three meals per day but is not eating as much due to recovering from a wrist fracture from a fall that happened 2 months ago. For breakfast, she will have ¾ cup of high-fiber cereal with ½ cup skim milk. For lunch, a heavy salad (chicken, cheese, romaine lettuce, vegetables) with light dressing, 1 slice of bread or a roll, and 4 ounces of wine. At dinner, she will have a big bowl of thickened soup/stew with bread or 2–3 ounces of fatty fish or meat, 1 cup of salad with light dressing, vegetables, and 4 ounces of wine. She tries to avoid milk-based foods due to the gas and bloating it causes and also tries to eat low-fat/low-salt to avoid gaining weight and increasing her blood pressure. She has no issues with chewing/swallowing or bowels aside from when eating milk-based foods. From her fall, the doctors performed a bone mineral density exam, in which her T-scores are as follows: for the hip: 1.7 (normal is > –1.0); for a vertebra: –2.6 (normal is > –2.5). Susan’s serum vitamin D level is 23 nmol/L. Her doctor has placed her on an over-the-counter 500-mg calcium with vitamin D supplement. She has prehypertension (average blood pressure of 128/92) and refuses to take any hypertension medications. She has lost 5 pounds over the past 2 months.
Height: 5’6”, weight: 122 pounds, weight history: 127 pounds (2 months ago)
Questions
In: Anatomy and Physiology
Smoky Mountain Corporation makes two types of hiking
boots—Xtreme and the Pathfinder. Data concerning these two product
lines appear below:
|
Xtreme |
Pathfinder |
||||||
|
Selling price per unit |
$ |
138.00 |
$ |
90.00 |
|||
|
Direct materials per unit |
$ |
64.40 |
$ |
51.00 |
|||
|
Direct labor per unit |
$ |
13.50 |
$ |
9.00 |
|||
|
Direct labor-hours per unit |
1.5 |
DLHs |
1.0 |
DLHs |
|||
|
Estimated annual production and sales |
22,000 |
units |
73,000 |
units |
|||
The company has a traditional costing system in which manufacturing
overhead is applied to units based on direct labor-hours. Data
concerning manufacturing overhead and direct labor-hours for the
upcoming year appear below:
|
Estimated total manufacturing overhead |
$ |
2,438,000 |
||
|
Estimated total direct labor-hours |
106,000 |
DLHs |
||
Required:
1. Compute the product margins for the Xtreme and the Pathfinder products under the company’s traditional costing system. (Do not round your intermediate calculations.)
|
2. The company is considering replacing its traditional costing
system with an activity-based costing system that would assign its
manufacturing overhead to the following four activity cost pools
(the Other cost pool includes organization-sustaining costs and
idle capacity costs):
.
|
Estimated |
Activity |
||||||||||||
|
Activities and Activity Measures |
Overhead Cost |
Xtreme |
Pathfinder |
Total |
|||||||||
|
Supporting direct labor (direct labor-hours) |
$ |
646,600 |
33,000 |
73,000 |
106,000 |
||||||||
|
Batch setups (setups) |
969,000 |
330 |
240 |
570 |
|||||||||
|
Product sustaining (number of products) |
780,000 |
1 |
1 |
2 |
|||||||||
|
Other |
42,400 |
NA |
NA |
NA |
|||||||||
|
Total manufacturing overhead cost |
$ |
2,438,000 |
|||||||||||
Compute the product margins for the Xtreme and the Pathfinder
products under the activity-based costing system. (Negative
product margins should be indicated with a minus sign. Round your
intermediate calculations to 2 decimal places.)
|
|||||||||
|
Xtreme |
Pathfinder |
Total |
|||||
|
% of |
% of |
||||||
|
Amount |
Total Amount |
Amount |
Total Amount |
Amount |
|||
|
Traditional Cost System |
|||||||
|
% |
% |
||||||
|
% |
% |
||||||
|
% |
% |
||||||
|
Total cost assigned to products |
$0 |
$0 |
0 |
||||
3. Prepare a quantitative comparison of the traditional and activity-based cost assignments. (Do not round intermediate calculations. Round your "Percentage" answer to 1 decimal place. (i.e. .1234 should be entered as 12.3))
|
Xtreme |
Pathfinder |
Total |
|||||
|
% of |
% of |
||||||
|
Amount |
Total Amount |
Amount |
Total Amount |
Amount |
|||
|
Activity-Based Costing System |
|||||||
|
Direct costs: |
|||||||
|
% |
% |
||||||
|
% |
% |
||||||
|
Indirect costs: |
|||||||
|
% |
% |
||||||
|
% |
% |
||||||
|
% |
% |
||||||
|
Total cost assigned to products |
$0 |
$0 |
$0 |
||||
|
Costs not assigned to products: |
|||||||
|
Total cost |
$0 |
||||||
In: Accounting
Smoky Mountain Corporation makes two types of hiking boots—the Xtreme and the Pathfinder. Data concerning these two product lines appear below:
| Xtreme | Pathfinder | |||||
| Selling price per unit | $ | 125.00 | $ | 91.00 | ||
| Direct materials per unit | $ | 64.20 | $ | 55.00 | ||
| Direct labor per unit | $ | 16.00 | $ | 10.00 | ||
| Direct labor-hours per unit | 1.6 | DLHs | 1.0 | DLHs | ||
| Estimated annual production and sales | 25,000 | units | 71,000 | units | ||
The company has a traditional costing system in which manufacturing overhead is applied to units based on direct labor-hours. Data concerning manufacturing overhead and direct labor-hours for the upcoming year appear below:
| Estimated total manufacturing overhead | $ | 2,331,000 | ||
| Estimated total direct labor-hours | 111,000 | DLHs | ||
Required:
1. Compute the product margins for the Xtreme and the Pathfinder products under the company’s traditional costing system. (Round your intermediate calculations to 2 decimal places and final answers to the nearest whole dollar amount.)
|
2. The company is considering replacing its traditional costing system with an activity-based costing system that would assign its manufacturing overhead to the following four activity cost pools (the Other cost pool includes organization-sustaining costs and idle capacity costs):
| Estimated Overhead Cost |
Expected Activity | |||||
| Activities and Activity Measures | Xtreme | Pathfinder | Total | |||
| Supporting direct labor (direct labor-hours) | $ | 888,000 | 40,000 | 71,000 | 111,000 | |
| Batch setups (setups) | 583,000 | 310 | 220 | 530 | ||
| Product sustaining (number of products) | 780,000 | 1 | 1 | 2 | ||
| Other | 80,000 | NA | NA | NA | ||
| Total manufacturing overhead cost | $ | 2,331,000 | ||||
2. Compute the product margins for the Xtreme and the Pathfinder products under the activity-based costing system. (Round your intermediate calculations to 2 decimal places.)
|
3. Prepare a quantitative comparison of the traditional and activity-based cost assignments.
Prepare a quantitative comparison of the traditional and activity-based cost assignments. (Round your intermediate calculations to 2 decimal places.)
|
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
In: Accounting
A diet doctor claims Australians are, on average, overweight by more than 10kg. To test this claim, a random sample of 100 Australians were weighed, and the difference between their actual weight and their ideal weight was calculated and recorded.
The data are contained in the Excel file Weights.xlsx.
Use these data to test the doctor's claim at the 5% level of significance.
| Excess weight (Kgs) |
| 16.0 |
| 4.0 |
| 4.0 |
| 4.5 |
| 11.0 |
| 7.0 |
| 7.0 |
| 16.5 |
| 14.5 |
| 5.5 |
| 16.5 |
| 0.5 |
| 13.5 |
| 26.0 |
| 28.0 |
| 31.5 |
| 14.0 |
| 25.0 |
| 14.5 |
| 1.0 |
| 2.5 |
| 4.0 |
| 17.5 |
| 6.0 |
| 5.0 |
| 4.5 |
| 10.0 |
| 11.0 |
| 8.0 |
| 0.5 |
| 4.5 |
| 10.5 |
| 31.0 |
| 23.0 |
| 11.5 |
| 10.0 |
| 10.0 |
| 22.5 |
| 4.0 |
| 12.5 |
| 29.5 |
| 23.5 |
| 10.5 |
| 10.5 |
| 10.0 |
| 12.5 |
| 21.5 |
| 5.0 |
| 5.0 |
| 20.0 |
| 15.0 |
| 15.0 |
| 25.0 |
| 15.0 |
| 11.0 |
| 28.5 |
| 14.0 |
| 24.5 |
| 20.0 |
| 7.5 |
| 1.5 |
| 5.5 |
| 9.5 |
| 3.0 |
| 8.5 |
| 4.0 |
| 5.5 |
| 8.5 |
| 17.0 |
| 13.0 |
| 20.5 |
| 23.0 |
| 18.5 |
| 16.5 |
| 6.5 |
| 5.0 |
| 16.5 |
| 5.0 |
| 9.0 |
| 15.0 |
| 21.0 |
| 9.0 |
| 24.0 |
| 8.0 |
| 9.0 |
| 6.5 |
| 23.0 |
| 7.5 |
| 14.5 |
| 15.5 |
| 0.5 |
| 10.0 |
| 23.0 |
| 21.0 |
| 7.5 |
| 15.0 |
| 10.5 |
| 8.5 |
| 16.5 |
| 17.0 |
Question 10
(Part B)
In this question, we let μ represent
| a. |
the population mean 12.7 |
|
| b. |
the population average ideal weight of Australians |
|
| c. |
the population average actual weight of Australians |
|
| d. |
the population average of difference between the actual and ideal weights |
|
| e. |
None of the above |
Question 11
(Part B)
The null hypothesis is
| a. |
H0: μ > 10 |
|
| b. |
H0: μ = 10 |
|
| c. |
H0: μ = 12.7 |
|
| d. |
H0: μ < 12.7 |
|
| e. |
None of the above |
Question 12
(Part B)
The alternative hypothesis is
| a. |
HA: μ > 10 |
|
| b. |
HA: μ < 12.7 |
|
| c. |
HA: μ ≠ 10 |
|
| d. |
HA: μ ≠ 12.7 |
|
| e. |
None of the above |
Question 13
(Part B)
The value of the t-statistic is
| a. |
–3.527 |
|
| b. |
0.3527 |
|
| c. |
3.527 |
|
| d. |
–0.275 |
|
| e. |
None of the above |
Question 14
(Part B)
The decision rule is
| a. |
reject HA if t > 1.984 |
|
| b. |
reject H0 if t > 1.984 |
|
| c. |
reject H0 if t < 1.660 |
|
| d. |
reject H0 if t > 1.660 |
|
| e. |
None of the above |
Question 15
(Part B)
The p-value is
| a. |
1.660 |
|
| b. |
0.05 |
|
| c. |
0.0003 |
|
| d. |
0.0070 |
|
| e. |
None of the above |
In: Math
The following data represent petal lengths (in cm) for independent random samples of two species of Iris. Petal length (in cm) of Iris virginica: x1; n1 = 35 5.1 5.6 6.2 6.1 5.1 5.5 5.3 5.5 6.9 5.0 4.9 6.0 4.8 6.1 5.6 5.1 5.6 4.8 5.4 5.1 5.1 5.9 5.2 5.7 5.4 4.5 6.4 5.3 5.5 6.7 5.7 4.9 4.8 5.7 5.1 Petal length (in cm) of Iris setosa: x2; n2 = 38 1.6 1.9 1.4 1.5 1.5 1.6 1.4 1.1 1.2 1.4 1.7 1.0 1.7 1.9 1.6 1.4 1.5 1.4 1.2 1.3 1.5 1.3 1.6 1.9 1.4 1.6 1.5 1.4 1.6 1.2 1.9 1.5 1.6 1.4 1.3 1.7 1.5 1.5 (a) Use a calculator with mean and standard deviation keys to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (b) Let μ1 be the population mean for x1 and let μ2 be the population mean for x2. Find a 99% confidence interval for μ1 − μ2. (Round your answers to two decimal places.) lower limit upper limit (c) Explain what the confidence interval means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 99% level of confidence, is the population mean petal length of Iris virginica longer than that of Iris setosa? Because the interval contains only positive numbers, we can say that the mean petal length of Iris virginica is longer. Because the interval contains only negative numbers, we can say that the mean petal length of Iris virginica is shorter. Because the interval contains both positive and negative numbers, we cannot say that the mean petal length of Iris virginica is longer. (d) Which distribution did you use? Why? The Student's t-distribution was used because σ1 and σ2 are unknown. The standard normal distribution was used because σ1 and σ2 are known. The standard normal distribution was used because σ1 and σ2 are unknown. The Student's t-distribution was used because σ1 and σ2 are known. Do you need information about the petal length distributions? Explain. Both samples are large, so information about the distributions is needed. Both samples are large, so information about the distributions is not needed. Both samples are small, so information about the distributions is needed. Both samples are small, so information about the distributions is not needed.
In: Math
The following data represent petal lengths (in cm) for independent random samples of two species of Iris. Petal length (in cm) of Iris virginica: x1; n1 =
35 5.1 5.8 6.5 6.1 5.1 5.5 5.3 5.5 6.9 5.0 4.9 6.0 4.8 6.1 5.6 5.1 5.6 4.8 5.4 5.1 5.1 5.9 5.2 5.7 5.4 4.5 6.4 5.3 5.5 6.7 5.7 4.9 4.8 5.9 5.1
Petal length (in cm) of Iris setosa: x2; n2 =
38 1.6 1.8 1.4 1.5 1.5 1.6 1.4 1.1 1.2 1.4 1.7 1.0 1.7 1.9 1.6 1.4 1.5 1.4 1.2 1.3 1.5 1.3 1.6 1.9 1.4 1.6 1.5 1.4 1.6 1.2 1.9 1.5 1.6 1.4 1.3 1.7 1.5 1.6
(a) Use a calculator with mean and standard deviation keys to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.)
x1 =
s1 =
x2 =
s2 =
(b) Let μ1 be the population mean for x1 and let μ2 be the population mean for x2. Find a 99% confidence interval for μ1 − μ2. (Round your answers to two decimal places.)
lower limit
upper limit
(c) Explain what the confidence interval means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 99% level of confidence, is the population mean petal length of Iris virginica longer than that of Iris setosa?
Because the interval contains only positive numbers, we can say that the mean petal length of Iris virginica is longer.
Because the interval contains only negative numbers, we can say that the mean petal length of Iris virginica is shorter.
Because the interval contains both positive and negative numbers, we cannot say that the mean petal length of Iris virginica is longer.
(d) Which distribution did you use? Why?
The Student's t-distribution was used because σ1 and σ2 are unknown.
The standard normal distribution was used because σ1 and σ2 are unknown.
The Student's t-distribution was used because σ1 and σ2 are known.
The standard normal distribution was used because σ1 and σ2 are known.
Do you need information about the petal length distributions? Explain.
Both samples are large, so information about the distributions is not needed
.Both samples are large, so information about the distributions is needed.
Both samples are small, so information about the distributions is needed.
Both samples are small, so information about the distributions is not needed.
In: Math