Question

There are a very large number of mutual funds from which an investor can choose. Each mutual fund has its own mix of different types of investments. The data below present the one-year return for the 13 best long-term bond funds and the 13 best world stock funds, according to the U.S. News & World Report. Analyze the data and determine whether any differences exist between long-term bond funds and world stock funds. (Use the 0.05 level of significance.)

Long Term Bond	World Stock
4.46	5.42
6.21	9.16
4.04	12.91
6.55	10.55
6.06	17.87
3.07	8.83
1.02	5.10
7.38	5.32
8.23	9.10
7.14	9.04
6.05	4.80
4.96	6.52
3.87	10.45

Answer 1

1) null and alternate hypothesis

H0:

H1:

2) level of significance = 0.05

3) test statistics

For long term bond

N1: 13
df1 = N - 1 = 13 - 1 = 12
M1: 5.31
SS1: 47.57
s21 = SS1/(N - 1) = 47.57/(13-1) = 3.96


For world stock

N2: 13
df2 = N - 1 = 13 - 1 = 12
M2: 8.85
SS2: 163.61
s22 = SS2/(N - 1) = 163.61/(13-1) = 13.63


T-value Calculation

s2p = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22) = ((12/24) * 3.96) + ((12/24) * 13.63) = 8.8

s2M1 = s2p/N1 = 8.8/13 = 0.68
s2M2 = s2p/N2 = 8.8/13 = 0.68

t = (M1 - M2)/√(s2M1 + s2M2) = -3.54/√1.35 = -3.04

4) p value = 0.0056

5) since p value less than level of significance so we reject null hypothesis.

So there sufficient evidence to conclude thay there significant differences exist between long-term bond funds and world stock funds.