2. Mrs. D who 27 years old plans to retire at the age of 55. Mrs. D would like to be able to withdraw $132,000 per year from her retirement account for 45 years after retirement beginning the year after her retirement. She is also expecting an inheritance of $54,000 to be transferred to her on her 35th birthday. a How much does she need to have in her retirement account by retirement date if the interest rate is 6% per year during the post-retirement years? b Suppose she already has $12,000 in her retirement investment account that earns 9% per year. What will be the value of this amount by her retirement date? c Given her goal, her expected inheritance, and the investment she already has in 1b, how much does she need to invest per year from now till retirement (at 9% annual rate of return) in order to reach her retirement goal?

27. Determine a venture’s sustainable growth rate based on the following information: sales = $1,000,000; net income = $150,000; common equity at the end of last year = $520,000; and the dividend payout percentage = 20%.

                        a.   10%

                        b.   16%

                        c.   20%

                        d. 24%

                        e.   30%

James Bond, Q, and M have agreed to meet at a pub after work for drinks. Bond cannot remember if they agreed to meet at the “Fanny on the Hill” or at “My Father’s Moustache” - so he tosses a coin to decide which pub to go to. Q is also in the same predicament; he tosses a coin to decide between “My Father’s Moustache” and “The Quiet Woman”. M faced with same quandary flips a coin first to decide whether or not he needs to head to the “Fanny on the Hill”. If the answer is “no”, then he flips again to decide between “My Father’s Moustache” and “The Quiet Woman”. What is the probability that

(a) Bond and Q meet? (b) Q and M meet? (c) all three meet? (d) all three go to different places? (e) at least two meet?

At an auto parts place, the inspection time for a vehicle is approximately normally distributed with the mean 25 minutes and the standard deviation 3

minutes.

1. What is the probability that a randomly selected car's inspection time

is between 20 and 31 minutes? Round your answer to three decimal places.

2. The owner of this auto parts places will give a gift card to the customer if his

car takes more than the longest 5% of the inspection time. What is the required

inspection time to get a gift card? Round your answer to three decimal places.

3. This place also offers a free car wash and the relationship between the car's

inspection time and washing time can be written as

            inspection time = 1.5 x washing time + 2.5

What are the mean and variance of total {inspection and washing} time?

Question 6 (this question has three parts (a), (b) & (c))

1. There are three securities (A, B and C) in the market. The covariance matrix and the standard deviations of the securities and the market are given in the following tables.

Covariance matrix

Standard deviation table

1. Calculate the correlation coefficient between:

1. A and B.
2. B and C.
3. A and C.
4. A and the market.
5. B and the market.
6. C and the market.

(Marks 1 x 6 = 6)

2. Calculate and explain the market risk for A, B and C.

(Marks 1 x 3 = 3)

3. Identify and explain the key differences between covariance, correlation and beta in interpreting risk-return relationships.

(Mark 1)

At an auto parts place, the inspection time for a vehicle is approximately normally distributed with the mean 25 minutes and the standard deviation 3 minutes.

1) What is the probability that a randomly selected car’s inspection time is between 20 and 31 minutes? Round your answer to three decimal places.

2) The owner of this auto parts places will give gift card to customer if his car takes more than the longest 5% of the inspection time. What is the required inspection time to get a gift card? Round your answer to three decimal places.

3) This place also offers free car wash, and the relationship between car’s inspection time and washing time can be written as

inspection time = 1.5 × washing time + 2.5

What are the mean and variance of total {inspection and washing} time.

1. The concentration of particles in a suspension is 49 per mL. A 5 mL volume of the suspension is withdrawn.

What is the probability that the number of particles withdrawn will be between 235 and 265?

2. a sample of 100 steel wires the average breaking strength is 46 kN, with a standard deviation of 2 kN.

Find a 95% confidence interval for the mean breaking strength of this type of wire. Round the answers to three decimal places.

The 95% confidence interval is (_,_ ).

Find a 99% confidence interval for the mean breaking strength of this type of wire. Round the answers to three decimal places.

The 99% confidence interval is (_,_ ).

An engineer claims that the mean breaking strength is between 45.7 kN and 46.3 kN. With what level of confidence can this statement be made? Express the answer as a percent and round to two decimal places.

The level of confidence is _%.

A new form of cognitive therapy has been developed to treat the symptoms of depression. To determine the effectiveness of the treatment, one group of individuals was exposed to the experimental treatment (Treatment Group) and a second unique group was not exposed to the new treatment (Control Group). The values below represent the Beck Depression Inventory (BDI) scores for the groups. The BDI is a widely used tool for screening depression, and higher scores indicate higher reported levels of depression.

Treatment Group

14 14 14 15 15 17 17 18 18 19

20 20 20 21 22 23 23 23 24 26

26 26 26 27 27 28 28 29 30 30

Control Group

15 15 17 19 19 20 21 22 22 23

24 24 24 24 24 25 25 25 26 26

27 27 27 29 29 29 30 31 31 32

34 34

1. What is the mean BDI score for the treatment group?

2.What is the mean BDI score for the control group?

3.What is the sum of squared deviations for the Treatment Group?

4.What is the sum of squared deviations for the Control Group?

5.Conduct a hypothesis test to determine whether the sample data provide evidence for a difference in the respective populations. Use a two-tailed test and an alpha level of .05. Be sure to include all steps in the hypothesis testing process. Report your findings in the following format:

Step 1
Ho:
Step 2
Identify critical value
Step 3
Report pooled variance
Report error term
Report test statistic (t score)
Step 4
Make a decision
Please show your work step by step so I can understand please and thank you! I will rate!

A new form of cognitive therapy has been developed to treat the symptoms of depression. To determine the effectiveness of the treatment, one group of individuals was exposed to the experimental treatment (Treatment Group) and a second unique group was not exposed to the new treatment (Control Group). The values below represent the Beck Depression Inventory (BDI) scores for the groups. The BDI is a widely used tool for screening depression, and higher scores indicate higher reported levels of depression.

Treatment Group

14 14 14 15 15 17 17 18 18 19

20 20 20 21 22 23 23 23 24 26

26 26 26 27 27 28 28 29 30 30

Control Group

15 15 17 19 19 20 21 22 22 23

24 24 24 24 24 25 25 25 26 26

27 27 27 29 29 29 30 31 31 32

34 34

1. What is the mean BDI score for the treatment group?

2.What is the mean BDI score for the control group?

3.What is the sum of squared deviations for the Treatment Group?

4.What is the sum of squared deviations for the Control Group?

5.Conduct a hypothesis test to determine whether the sample data provide evidence for a difference in the respective populations. Use a two-tailed test and an alpha level of .05. Be sure to include all steps in the hypothesis testing process. Report your findings in the following format:

Step 1
Ho:
Step 2
Identify critical value
Step 3
Report pooled variance
Report error term
Report test statistic (t score)
Step 4
Make a decision
Please show your work step by step so I can understand please and thank you! I will rate!

A new form of cognitive therapy has been developed to treat the symptoms of depression. To determine the effectiveness of the treatment, one group of individuals was exposed to the experimental treatment (Treatment Group) and a second unique group was not exposed to the new treatment (Control Group). The values below represent the Beck Depression Inventory (BDI) scores for the groups. The BDI is a widely used tool for screening depression, and higher scores indicate higher reported levels of depression.

Treatment Group

14 14 14 15 15 17 17 18 18 19

20 20 20 21 22 23 23 23 24 26

26 26 26 27 27 28 28 29 30 30

Control Group

15 15 17 19 19 20 21 22 22 23

24 24 24 24 24 25 25 25 26 26

27 27 27 29 29 29 30 31 31 32

34 34

1. What is the mean BDI score for the treatment group?

2.What is the mean BDI score for the control group?

3.What is the sum of squared deviations for the Treatment Group?

4.What is the sum of squared deviations for the Control Group?

5.Conduct a hypothesis test to determine whether the sample data provide evidence for a difference in the respective populations. Use a two-tailed test and an alpha level of .05. Be sure to include all steps in the hypothesis testing process. Report your findings in the following format:

Step 1
Ho:
Step 2
Identify critical value
Step 3
Report pooled variance
Report error term
Report test statistic (t score)
Step 4
Make a decision
Please show your work step by step so I can understand please and thank you! I will rate!

A new form of cognitive therapy has been developed to treat the symptoms of depression. To determine the effectiveness of the treatment, one group of individuals was exposed to the experimental treatment (Treatment Group) and a second unique group was not exposed to the new treatment (Control Group). The values below represent the Beck Depression Inventory (BDI) scores for the groups. The BDI is a widely used tool for screening depression, and higher scores indicate higher reported levels of depression.

Treatment Group

14 14 14 15 15 17 17 18 18 19

20 20 20 21 22 23 23 23 24 26

26 26 26 27 27 28 28 29 30 30

Control Group

15 15 17 19 19 20 21 22 22 23

24 24 24 24 24 25 25 25 26 26

27 27 27 29 29 29 30 31 31 32

34 34

1. What is the mean BDI score for the treatment group?

2.What is the mean BDI score for the control group?

3.What is the sum of squared deviations for the Treatment Group?

4.What is the sum of squared deviations for the Control Group?

5.Conduct a hypothesis test to determine whether the sample data provide evidence for a difference in the respective populations. Use a two-tailed test and an alpha level of .05. Be sure to include all steps in the hypothesis testing process. Report your findings in the following format:

Step 1
Ho:
Step 2
Identify critical value
Step 3
Report pooled variance
Report error term
Report test statistic (t score)
Step 4
Make a decision
Please show your work step by step so I can understand please and thank you! I will rate!

16. Suppose you run a between-subjects experiment in which 11 subjects are randomly selected from the same parent population. 5 subjects are assigned to the control group and 6 subjects are assigned to the experimental group. The subjects in the experimental group are given an experimental drug that is supposed improve their coordination. After giving the experimental group the drug, you measure the coordination of all 11 subjects on a scale for which a higher score means better coordination. The coordination scores for 5 subjects in the control group are 49, 53, 67, 81, 43. The coordination scores for the 6 subjects in the experimental group are 58, 63, 92, 80, 67, 74. What are the degrees of freedom for the control group, and the experimental group, as well as the total degrees of freedom for this analysis.

17. What is the value of the pooled variance for the problem described in Question 16?

18. What is the value of sdifferrence for the data in Question 16?

19. Calculate the t statistic for the data in Question 16.

20. Does your t statistic allow you to reject that the null hypothesis that the drug had no effect in favor of your experimental hypothesis that the drug improves coordination at an alpha level of 0.05? What about at an alpha level of 0.01?