4 Consider the following rates of return for one year in per

4. Consider the following rates of return for one year (in percent) for a sample of 12 mutual funds. 4.63, 4.15, 4.76, 4.70, 4.65, 4.52, 4.70, 5.06, 4.42, 4.51, 4.24, 4.52 Using the 0.05 significance level, is it reasonable to conclude that the mean rate of return is more than 4.50% (use hypothesis testing to answer this question)?

Solution

Set Up Hypothesis
Null, mean rate is same as 4.5 H0: U=4.5
Alternate,mean rate is more than 4.5 H1: U>4.5
Test Statistic
Population Mean(U)=4.5
Sample X(Mean)=4.57167
Standard Deviation(S.D)=0.2405
Number (n)=12
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =4.57167-4.5/(0.2405/Sqrt(11))
to =1.032
| to | =1.032
Critical Value
The Value of |t | with n-1 = 11 d.f is 1.7959
We got |to| =1.032 & | t | =1.7959
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Right Tail - Ha : ( P > 1.0323 ) = 0.16204
Hence Value of P0.05 < 0.16204,Here We Do not Reject Ho

We don\'t have evidence to support mean rate is more than 4.5