Question 1 - Part A
A company employs a total of 6,000 employs and wants you, the designated researcher to conduct a survey involving 300 employees.
Required:
Explain how you would go about selecting this sample using various sampling techniques.
Question 1 - Part B
A population has a mean of 60 and a standard deviation of 10 and a random sample of 70 are taken.
Required:
What is the probability that the sample mean is each of the following?
a) Greater than 65
b) Less than 61
c) Less than 58
d) Between 58.5 and 62.3
e) Between 61.5 and 63.3
Question 2 - Part A
Required:
Use the following information to construct the confidence intervals specified to estimate µ.
a) 98% confidence for x- = 20, σ = 3.5 and n = 60
b) 95% confidence for x- = 120, σ = 24 and n = 75
c) 80% confidence for x- = 4, σ = 0.974 and n = 30
d) 90% confidence for x- = 47.8, σ = 8.4 and n = 45
Question 2 - Part B
Required:
If a random sample of 52 items produces x- = 138.4 and S = 20.6, what is the 98% confidence interval for µ?
Assume x is normally distributed for the population. What is the point estimate?
Question 2 - Part C
Required:
Determine the sample size necessary to estimate p for the following information:
a) E = 0.04, p is approximately 0.38 and confidence interval is 96%.
b) E is to be within 0.06, p is unknown and confidence interval is 95%.
c) E is to be within 7%, p is approximately 60% and confidence interval is 90%.
d) E is to be no more than 0.02, p is unknown, and confidence interval is 99%.
Question 3 - Part A
Required:
a) Use the date given to test the following hypotheses.
??0 : µ = 22 ???? : µ ≠ 22
x- = 27.8, σ = 8.46, and n = 45, α = 0.01
b) Use the p-value to reach a statistical conclusion.
c) Using the critical value method, what are the critical sample mean values?
Question 3 - Part B
Required:
A random sample of size 25 is taken, resulting in a sample mean of 16.55 and a sample standard deviation of 3.89. Assume x is normally distributed and use this information and α = 0.05 to test the following hypotheses:
??0 : µ = 16 ???? : µ ≠ 16.
Question 4
Required:
Sketch a scatter plot from the following data and determine the equation of the regression line:
| x |
22 |
31 |
38 |
12 |
18 |
| y |
17 |
25 |
20 |
18 |
23 |
Question 5
You have been provided with the following information:
| Case |
Single cash flow $ |
Interest rate % |
Deposit period (years) |
| A |
5,500 |
8 |
7 |
| B |
11,000 |
9 |
10 |
| C |
26,000 |
10 |
12 |
| D |
45,000 |
12 |
9 |
Required:
For each of the cases shown in the above table, calculate the future value of a single cash flow deposited today that will be available at the end of the deposit period if the interest is compounded annually at the rate specified over the given period.
Question 5 - Part B
You have been provided with the following information:
| Case |
Single cash flow $ |
Discount rate % |
End of period (years) |
| A |
30,000 |
8 |
20 |
| B |
12,000 |
14 |
12 |
| C |
160,000 |
11 |
6 |
| D |
50,000 |
20 |
8 |
Required:
For each of the cases shown in the above table, calculate the present value of the cash flow, discounting at the rate given and assuming that the cash flow is received at the end of the period noted.
Question 5 - Part C
You have been provided with the following information:
| Case |
Amount of annuity $ |
Interest rate % |
Deposit period (years) |
| A |
31,000 |
20 |
5 |
| B |
12,000 |
9 |
8 |
| C |
7,000 |
14 |
30 |
| D |
3,000 |
8 |
10 |
Required:
a) Calculate the future value of the annuity assuming that it is:
i. An ordinary annuity
ii. An annuity due.
b) Compare your findings in parts a) i) and a) ii). All else being identical, which type of annuity is preferable? Explain why.
Question 5 - Part D
You have been provided with the following information:
| Case |
Amount of annuity $ |
Interest rate % |
Period (years) |
| A |
$10,000 |
7% |
3 |
| B |
50,000 |
12 |
15 |
| C |
145,000 |
5 |
7 |
| D |
27,500 |
10 |
5 |
Required:
c) Calculate the present value of the annuity assuming that it is:
iii. An ordinary annuity
iv. An annuity due.
d) Compare your findings in parts a) i) and a) ii). All else being identical, which type of annuity is preferable? Explain why.
Question 5 - Part E
You have been provided with the following information:
| Loan |
Principal $ |
Interest rate % |
Term of loan(years) |
| A |
$15,000 |
8% |
3 |
| B |
63,000 |
12 |
10 |
| C |
78,000 |
10 |
30 |
| D |
7,000 |
15 |
5 |
Required:
For each of the cases shown in the above table, calculate the equal end of year payment required each year, over the life of the loans shown in the following table, to repay them fully during the stated term of the loan.