Question

. Is there a difference in the yields of different types of investments? The accompanying data provide yields for a one-year certificate of deposit (CD) and a five-year CD for 25 banks. Complete parts a through c below. Click the icon to view the yields for one-year CDs and five-year CDs. a. Construct a 90% confidence interval estimate for the mean yield of one-year CDs. sus(Type integers or decimals rounded to two decimal places as needed.) b. Construct a 90% confidence interval estimate for the meanfield of five-year CDs. sus (Type integers or decimals rounded to two decimal places as needed.) c. Compare the results of (a) and (b).

Answer 1

Answer(a):

For one year CD:

Bank	One-Year CD(x)	x2
1	0.5	0.25
2	0.8	0.64
3	0.85	0.7225
4	0.4	0.16
5	0.45	0.2025
6	0.2	0.04
7	0.45	0.2025
8	2	4
9	0.85	0.7225
10	0.6	0.36
11	0.45	0.2025
12	0.55	0.3025
13	0.3	0.09
14	0.6	0.36
15	1.75	3.0625
16	1	1
17	1.6	2.56
18	2.2	4.84
19	1.1	1.21
20	1.05	1.1025
21	0.5	0.25
22	0.5	0.25
23	0.2	0.04
24	1.1	1.21
25	2.1	4.41
Total	22.1	28.19

n=25

Sample mean

22.1. EL Σ 1. 25

T = 0.884

The standard deviation of sample is given by

Σχ2 (Σx) n S = η –1

28.19 – (22.1)?/25 S= 25 - 1

S 28.19 – 19.5364 24 V

s= 0.360567

s = 0.60

The 90% confidence interval of mean of one-year CD is given by

x+ta/2, -1) * se(x)

S 0.884 + (0.95,24) * n

0.884 +1.7109 0.60 V25

0.884±1.7109 * 0.12

0.884±0.2055

Lower limit= 0.68

Upper limit = 1.09

Hence the 90% Confidence interval estimate for the mean yield of one year CDs

0.68≤µ≤1.09

Answer(b):

For Five year CDs

Bank	Five-Year CD(x)	x2
1	4.75	22.5625
2	4.95	24.5025
3	4.9	24.01
4	3.3	10.89
5	4.1	16.81
6	3.9	15.21
7	3.85	14.8225
8	4.45	19.8025
9	4.7	22.09
10	4.15	17.2225
11	4.6	21.16
12	3.5	12.25
13	4.3	18.49
14	5.05	25.5025
15	4.1	16.81
16	4.2	17.64
17	5.1	26.01
18	4.65	21.6225
19	5.1	26.01
20	4.45	19.8025
21	4.45	19.8025
22	4.05	16.4025
23	3.5	12.25
24	4.5	20.25
25	3.95	15.6025
Total	108.55	477.5275

n=25

Sample mean

Σ 108.55 Υ = η 25

T = 4.342

The standard deviation of sample is given by

Σχ2 (Σx) n S = η –1

(108.55)/25 477.5275 - S= 25 - 1

S 477.5275 - 471.3241 24 V

s= V0.2585

s=0.5084

The 90% confidence interval of mean of five-year CD is given by

x+ta/2, -1) * se(x)

S 4.342 + (0.95,24) * n

0.5084 4.342 +1.7109 * V25

4.342 +1.7109 * 0.1017

4.342 +0.174

Lower limit= 4.17

Upper limit = 4.52

Hence the 90% Confidence interval estimate for the mean yield of five year CDs

4.17≤µ≤4.52

Answer(c): we can observe that the 90% confidence interval of means of one year CD and five year CD does not overlap and also we can see that the upper limit of 90% CI of one year CDs mean is less than the lower limit of 90% CI of five year CDs mean.

The correct option is

B. one can be 90% confident that the mean yield of one year CD is less than the mean yield of five year CDs.