Research Scenario: You have been raising Bombina orientalis, or Oriental fire-bellied toads, and measured the frogs’ jumps in centimeters. Your latest study looks at males and females’ reactions to being raised in a room with another animal. You set up three terrariums, each with six male and six female frogs. Each terrarium is in a separate room. Let A1 = male frogs, A2 =female frogs, B1 = frogs raised in a room with a dog, B2 = frogs raised in a room with a cat, and B3 = frogs raised in a room with a parrot.

	B1	B2	B3
A1	45	23	39
	42	30	27
	41	31	31
	48	23	27
	42	33	37
	43	36	24
A2	32	36	49
	29	43	48
	31	37	44
	33	25	43
	25	32	36
	34	40	44

1. Restate the research and null hypothesis for each variable (and don’t forget the interaction).

2. What are the degrees of freedom of the F distribution for each variable and the interaction?

3. What is the value of F for the two main effects?

4. Is there a significant main effect of roommate? Explain and support your position.

5. Is there a significant main effect of gender? Explain and support your position.

6. Is there a significant interaction between the sex of the frogs and the species of roommate? Explain and support your position.

7. Fill in the appropriate cell, column, and row means in the table below. Then fill in the appropriate seventeen terms in the ANOVA summary table (or simply paste the table from SPSS).

Table of Means

	B1	B2	B3
A1
A2

                                                                  

ANOVA Summary Table
Source	df	ss	MS	F
A
B
AB
Within
Total

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.4%. The probability distributions of the risky funds are:

	Expected Return	Standard Deviation
Stock fund (S)	15%	44%
Bond fund (B)	8%	38%

The correlation between the fund returns is .0684.

A) Suppose now that your portfolio must yield an expected return of 13% and be efficient, that is, on the best feasible CAL. -What is the standard deviation of your portfolio?

B) What is the proportion invested in the T-bill fund?

C) What is the proportion invested in each of the two risky funds?

Stock %

Bonds %

A publisher reports that 65% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually less than the reported percentage. A random sample of 160 found that 60% of the readers owned a laptop. Is there sufficient evidence at the 0.02 level to support the executive's claim?

Step 1 of 7:

State the null and alternative hypotheses.

Step 2 of 7:

Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 7:

Specify if the test is one-tailed or two-tailed.

Step 4 of 7:

Determine the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 7:

Identify the value of the level of significance.

Step 6 of 7:

Make the decision to reject or fail to reject the null hypothesis.

Step 7 of 7:

State the conclusion of the hypothesis test.

A publisher reports that 23% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually above the reported percentage. A random sample of 300 found that 29% of the readers owned a personal computer. Is there sufficient evidence at the 0.10 level to support the executive's claim?

Step 1 of 7:

State the null and alternative hypotheses.

Step 2 of 7:

Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 7:

Specify if the test is one-tailed or two-tailed.

Step 4 of 7:

Determine the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 7:

Identify the value of the level of significance.

Step 6 of 7:

Make the decision to reject or fail to reject the null hypothesis.

Step 7 of 7:

State the conclusion of the hypothesis test.

Test the given claim. Assume that a simple random sample is selected from a normally distributed population. Use either the​ P-value method or the traditional method of testing hypotheses.

Company A uses a new production method to manufacture aircraft altimeters. A simple random sample of new altimeters resulted in errors listed below. Use a 0.05 level of significance to test the claim that the new production method has errors with a standard deviation greater than 32.2​ ft, which was the standard deviation for the old production method. If it appears that the standard deviation is​ greater, does the new production method appear to be better or worse than the old​ method? Should the company take any​ action?

negative 44−44​,

7777​,

negative 23−23​,

negative 74−74​,

negative 45−45​,

1414​,

1919​,

5252​,

negative 8−8​,

negative 55−55​,

negative 107−107​,

negative 107−107  

Find the test statistic.

chi squaredχ2equals=nothing

​(Round to two decimal places as​ needed.)

Determine the critical​ value(s).

The critical​ value(s) is/are

nothing.

​(Use a comma to separate answers as needed. Round to two decimal places as​ needed.)

Since the test statistic is

▼

less than

between

equal to

greater than

the critical​ value(s),

▼

rejectreject

fail to rejectfail to reject

Upper H 0H0.

There is

▼

insufficient

sufficient

evidence to support the claim that the new production method has errors with a standard deviation greater than 32.2 ft.

The variation appears to be

▼

greater

less

about the same

than in the​ past, so the new method appears to be

▼

better

worse

similar

​, because there will be  

▼

fewer

more

the same number of

altimeters that have errors.​ Therefore, the company

▼

should

should not

take immediate action to reduce the variation.

1. For the table below, fill in the missing sections for the Mean, Median, Mode, Range, and Standard Deviation on your own. Remember to round to two decimal places.

Hint: Put it in SPSS to simplify the calculation of the standard deviation, using the “Means” test under the Analyze menu!

Then complete the five questions and transfer your answers to the quiz in Canvas

Condition 1 Scores Condition 2 Scores

4, 1, 2, 4, 2, 3, 7, 4, 3, 5, 8, 3 4, 4, 5, 3, 3, 2, 3, 6, 4, 7, 8, 10

Column Mean

Column Median

Column Mode

Standard Deviation

Column Range

1. The correct mean for Condition One is _______ while the correct mean for Condition Two is ______:

A. 4.92 and 3.83

B. 5.17 and 3.42

C. 3.50 and 4.00

D. 3.83 and 4.92

E. 2.04 and 2.39

2. The correct standard deviation for Condition One is ________ while the correct standard deviation for

Condition Two is _______

A. 4.92 and 3.83

B. 5.17 and 3.42

C. 3.50 and 4.00

D. 3.83 and 4.92

E. 2.04 and 2.39

3. Which of the following is true about the mode?

A. Condition One has one mode while Condition Two has two modes

B. Condition Two has one mode while Condition One has two modes

C. The mode(s) for Conditions One and Two are different

D. The mode(s) for Conditions One and Two are the same

4. What is the best interpretation for this t-Test?

A. It was significant,

t

(21.46) = 1.19,

p

< .05

B. It was significant,

t

(22) = 1.19,

p

< .05

C. It was significant,

t

(22) = 0.56,

p

< .001

D. It was not significant,

t

(21.46) = 1.19,

p

> .05

E. It was not significant,

t

(22) = 1.19,

p

> .05

5. Use the Independent Samples Test table as well as your findings for the mean and SDs (from question

#1) to determine which of the following is

t

-Test write-ups correct:

A. We ran an independent samples

t

-Test with score as the dependent variable and condition (1

versus 2) as the independent variable, which was significant,

t

(21.46) = 1.19,

p

< .05. Scores

were higher in condition 1 (

M

= 3.83,

SD

= 2.04) than in condition 2 (

M

= 4.92,

SD

= 2.39).

B. We ran an independent samples

t

-Test with score as the dependent variable and condition (1

versus 2) as the independent variable, which was significant,

t

(22) = 1.19,

p

< .05. Scores were

higher in condition 1 (

M

= 4.92,

SD

= 2.39) than in condition 2 (

M

= 3.83,

SD

= 2.04).

C. We ran an independent samples

t

-Test with score as the dependent variable and condition (1

versus 2) as the independent variable, which was significant,

t

(22) = 1.19,

p

< .05. Scores were

higher in condition 1 (

M

= 3.83,

SD

= 2.04) than in condition 2 (

M

= 4.92,

SD

= 2.39).

D. We ran an independent samples

t

-Test with score as the dependent variable and condition (1

versus 2) as the independent variable, which was not significant,

t

(21.46) = 0.56,

p

> .05. Scores

were higher in condition 1 (

M

= 3.83,

SD

= 2.04) than in condition 2 (

M

= 4.92,

SD

= 2.39).

E. We ran an independent samples

t

-Test with score as the dependent variable and condition (1

versus 2) as the independent variable, which was not significant,

t

(22) = 1.19,

p

> .05. Scores did

not differ significantly between condition 1 (

M

= 3.83,

SD

= 2.04) and condition 2 (

M

= 4.92,

SD

= 2.39).

6. Last year LaCroix Optical had $145 million of sales, and it had $40 million of fixed assets that were used at 75% of capacity. Use this information to solve the next two problems.

1. In millions, by how much could LaCroix Optical sales increase before it is required to increase its fixed assets?
   
   
2. LaCroix Optical was approached by the Department of Defense (DoD)because of their ability to manufacture the lens required for night vision goggles. LaCroix Optical is the last remaining firm domiciled in the United States that can manufacture the night vision lens, and subsequently the DoD designated the company as essential critical infrastructure. The company’s sales are expected to approximately double after signing a DoD contract. How much additional financing will LaCroix Optical need?     

Albatross Airlines’ fixed operating costs are $5.8 million, and its variable cost ratio is 0.20. The firm has $2 million in bonds outstanding with a coupon interest rate of 8 percent. Albatross has 300,000 shares of common stock outstanding. Revenues for the firm are $8 million, and the firm is in the 40 percent corporate income tax bracket. Compute the degree of operating leverage for the firm.

Using the information in the previous question, calculate the degree of financial leverage for Albatross Airlines.

Using the information in the two previous questions, calculate what Albatross’s EPS would be if the firm’s sales were to increase by 5%.

Hint: you first need to calculate the current EPS and then calculate the %change in EPS due to the 5% change in sales. Then, use the two to calculate the new EPS level.

A pendulum consists of a light rigid rod of length 250 mm, with two identical uniform solid spheres of radius 50 mm attached one on either side of its lower end. Find the period of small oscillations (a) perpendicular to the line of centers and (b) along it.

PRO FORMA INCOME STATEMENT

At the end of last year, Roberts Inc. reported the following income statement (in millions of dollars):

Sales	$3,000
Operating costs excluding depreciation	2,450
EBITDA	$550
Depreciation	250
EBIT	$300
Interest	125
EBT	$175
Taxes (40%)	70
Net income	$105

Looking ahead to the following year, the company's CFO has assembled this information:

• Year-end sales are expected to be 14% higher than the $3 billion in sales generated last year.
• Year-end operating costs, excluding depreciation, are expected to equal 80% of year-end sales.
• Depreciation is expected to increase at the same rate as sales.
• Interest costs are expected to remain unchanged.
• The tax rate is expected to remain at 40%.

On the basis of that information, what will be the forecast for Roberts' year-end net income? Enter your answer in millions. For example, an answer of $25,000,000 should be entered as 25. Round your answer to two decimal places.

$___ million