Question

A sample containing years to maturity and yield for  corporate bonds are contained in the data given below.

Years to Maturity		Yield		Years to Maturity		Yield
5.75		7.728		3.25		2.820
25.25		2.415		5.25		4.835
1.75		5.382		15.75		6.905
23.50		5.106		1.50		4.849
26.25		1.576		23.75		5.054
18.50		7.145		2.50		3.966
20.50		0.811		14.25		5.300
29.75		4.275		16.50		3.114
1.50		7.320		24.75		5.949
5.75		8.140		11.50		2.934
13.50		5.170		21.50		6.921
14.50		7.286		27.75		7.810
13.25		3.505		14.25		6.998
6.25		7.009		12.00		7.759
13.75		7.062		14.00		3.196
10.75		7.764		27.50		1.789
12.75		7.687		17.75		8.066
29.50		1.145		22.75		3.984
6.75		1.055		13.25		3.992
28.25		5.902		17.00		0.794

a. What is the sample mean years to maturity for corporate bonds and what is the sample standard deviation?

Mean	(to 4 decimals)
Standard deviation	(to 4 decimals)

b. Develop a  confidence interval for the population mean years to maturity. Round the answer to four decimal places.

  ,   years

c. What is the sample mean yield on corporate bonds and what is the sample standard deviation?

Mean	(to 4 decimals)
Standard deviation	(to 4 decimals)

d. Develop a  confidence interval for the population mean yield on corporate bonds. Round the answer to four decimal places.

  ,   percent

Answer 1

Years to Maturity		Yield
Mean	15.3625	Mean	5.01295
Standard Error	1.352465	Standard Error	0.366903
Median	14.25	Median	5.138
Mode	5.75	Mode	#N/A
Standard Deviation	8.553742	Standard Deviation	2.320498
Sample Variance	73.16651	Sample Variance	5.384711
Kurtosis	-1.01337	Kurtosis	-1.09878
Skewness	0.019778	Skewness	-0.35711
Range	28.25	Range	7.346
Minimum	1.5	Minimum	0.794
Maximum	29.75	Maximum	8.14
Sum	614.5	Sum	200.518
Count	40	Count	40

• a) Sample mean years to maturity

• Mean=15.3625

• Sample standard deviation years to maturity

• Std DEv= 8.553742

b) : Population mean years to maturity.

Since population standard deviation is not known. We use t distribution to find confidence interval for population mean.

The 95% confidence interval for population mean years is to maturity is

Alpha: level of significance = 0.05

From t-table

Hence 95% confidence interval is

=(15.3625 -8.553742*2.0227/sqrt(40) ,15.3625 -8.553742*2.0227/sqrt(40))

=(12.6269,18.0981)

95% confidence interval for population mean years to maturity is (12.6269,18.0981) years.

c) Sample mean yield on corporate bond

5.01295

Sample standard deviation yield on corporate bond

2.320498

d) : Population mean yield on corporate bond

Since population standard deviation is not known. We use t distribution to find confidence interval for population mean.

The 95% confidence interval for population mean yield on corporate bond is

Alpha: level of significance = 0.05

From t-table

Hence 95% confidence interval is

=(5.01295 -2.320498*2.0227/sqrt(40) ,5.01295 +2.320498*2.0227/sqrt(40))

=(4.2708,5.7551)

95% confidence interval for population mean yield on corporate bond is (4.2708,5.7551) percent.