The average annual total return for US Diversified Equity mutual funds from 1999

Question

The average annual total return for US Diversified Equity mutual funds from 1999 to 2003 was 4.1% (BusinessWeek, January 26, 2004). A researcher would like to conduct a hypothesis test to see whether the returns for mid-cap growth funds over the same period are significantly different from the average for US Diversified Equity funds.

a) Formulate the hypotheses that can be used to determine whether the mean annual return for mid- cap growth funds differ from the mean for US Diversified Equity funds.

b) A sample of 40 mid-cap growth funds provides a mean return of x = 3.4%. Assume the population standard deviation for mid-cap growth funds is known from previous studies to be 2% . Use the sample results to compute the test statistic and p-value for the hypothesis test

b) At = 0.05, what is your conclusion?

Explanation / Answer

Given that,
population mean(u)=4.1
standard deviation, =2
sample mean, x =3.4
number (n)=40
null, Ho: =4.1
alternate, H1: !=4.1
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 3.4-4.1/(2/sqrt(40)
zo = -2.21359
| zo | = 2.21359
critical value
the value of |z | at los 5% is 1.96
we got |zo| =2.21359 & | z | = 1.96
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != -2.21359 ) = 0.02686
hence value of p0.05 > 0.02686, here we reject Ho

ANSWERS
---------------
a.
null, no diffrence between mean annual return for mid- cap growth,US Diversified Equity funds Ho: =4.1
alternate,the mean annual return for mid- cap growth funds differ from the mean for
US Diversified Equity funds H1: !=4.1

b.
test statistic: -2.21359
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0.02686
we conclude that, mean annual return for mid- cap growth funds differ from the mean for
US Diversified Equity funds

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