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 b below.

Bank   One-Year CD   Five-Year CD
1   0.45   4.90
2   0.75   4.95
3   0.85   4.90
4   0.25   3.25
5   0.35   4.05
6   0.20   4.00
7   0.50   3.80
8   2.05   4.40
9   0.65   4.70
10   0.75   4.00
11   0.40   4.50
12   0.55   3.50
13   0.25   4.20
14   0.60   5.00
15   1.70   4.10
16   1.00   4.30
17   1.40   4.95
18   2.20   4.70
19   1.05   4.95
20   0.90   4.40
21   0.60   4.40
22   0.50   4.10
23   0.35   3.50
24   1.10   4.35
25   1.90   4.05

a. Construct a 95​% confidence interval estimate for the mean yield of​ one-year CDs.

b. Construct a 95​% confidence interval estimate for the mean yield of​ five-years CDs.

Answer 1

a) For one-year CD's:

∑x = 21.3

∑x² = 26.19

n = 25

Mean , x̅ = Ʃx/n = 21.3/25 = 0.8520

Standard deviation, s = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(26.19-(21.3)²/25)/(25-1)] = 0.5789

95% Confidence interval :

At α = 0.05 and df = n-1 = 24, two tailed critical value, t-crit = T.INV.2T(0.05, 24) = 2.064

Lower Bound = x̅ - t-crit*s/√n = 0.852 - 2.064 * 0.5789/√25 = 0.61

Upper Bound = x̅ + t-crit*s/√n = 0.852 + 2.064 * 0.5789/√25 = 1.09

0.61 < µ < 1.09

b) For Five years CD's:

∑x = 107.95

∑x² = 472.0175

n = 25

Mean , x̅ = Ʃx/n = 107.95/25 = 4.3180

Standard deviation, s = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(472.0175-(107.95)²/25)/(25-1)] = 0.4954

95% Confidence interval :

At α = 0.05 and df = n-1 = 24, two tailed critical value, t-crit = T.INV.2T(0.05, 24) = 2.064

Lower Bound = x̅ - t-crit*s/√n = 4.318 - 2.064 * 0.4954/√25 = 4.11

Upper Bound = x̅ + t-crit*s/√n = 4.318 + 2.064 * 0.4954/√25 = 4.52

4.11 < µ < 4.52