In: Math
(Data below) (to be done with EVIEWS or any data processor)
Millions of investors buy mutual funds, choosing from thousands of possibilities. Some funds can be purchased directly from banks or other financial institutions (direct) whereas others must be purchased through brokers (broker), who charge a fee for this service. A group of researchers randomly sampled 50 annual returns from mutual funds that can be acquired directly and 50 from mutual funds that are bought through brokers and recorded their net annual returns (NAR, %), which are the returns on investment after deducting all relevant fees.1
(a) In general, we can conduct hypothesis tests on a population central location with EViews by performing the (one sample) t-test, the sign test or the Wilcoxon signed ranks test.2 Suppose we would like to know whether there is evidence at the 5% level of significance that the population central location of NAR is larger than 5%. Which test(s) offered by EViews would be the most appropriate this time? Explain your answer by considering the conditions required by these tests.
(b) Perform the test you selected in part (e) above with EViews. Do not forget to specify the null and alternative hypotheses, to identify the test statistic, to make a statistical decision based on the p-value, and to draw an appropriate conclusion. If the test relies on normal approximation, also discuss whether this approximation is reasonable this time.
(c) Perform the other tests mentioned in part (a). Again, do not forget to specify the null and alternative hypotheses, to identify the test statistics, to make statistical decisions based on the p-values, and to draw appropriate conclusions. Also, if the tests rely on normal approximation, discuss whether these approximations are reasonable this time.
(d) Compare your answers in parts (b) and (c) to each other. Does it matter in this case whether the population of net returns is normally, or at least symmetrically distributed or not? Explain your answer.
PURCHASE | NAR (%) |
Direct | 9.33 |
Direct | 6.94 |
Direct | 16.17 |
Direct | 16.97 |
Direct | 5.94 |
Direct | 12.61 |
Direct | 3.33 |
Direct | 16.13 |
Direct | 11.20 |
Direct | 1.14 |
Direct | 4.68 |
Direct | 3.09 |
Direct | 7.26 |
Direct | 2.05 |
Direct | 13.07 |
Direct | 0.59 |
Direct | 13.57 |
Direct | 0.35 |
Direct | 2.69 |
Direct | 18.45 |
Direct | 4.23 |
Direct | 10.28 |
Direct | 7.10 |
Direct | 3.09 |
Direct | 5.60 |
Direct | 5.27 |
Direct | 8.09 |
Direct | 15.05 |
Direct | 13.21 |
Direct | 1.72 |
Direct | 14.69 |
Direct | 2.97 |
Direct | 10.37 |
Direct | 0.63 |
Direct | 0.15 |
Direct | 0.27 |
Direct | 4.59 |
Direct | 6.38 |
Direct | 0.24 |
Direct | 10.32 |
Direct | 10.29 |
Direct | 4.39 |
Direct | 2.06 |
Direct | 7.66 |
Direct | 10.83 |
Direct | 14.48 |
Direct | 4.80 |
Direct | 13.12 |
Direct | 6.54 |
Direct | 1.06 |
Broker | 3.24 |
Broker | 6.76 |
Broker | 12.80 |
Broker | 11.10 |
Broker | 2.73 |
Broker | 0.13 |
Broker | 18.22 |
Broker | 0.80 |
Broker | 5.75 |
Broker | 2.59 |
Broker | 3.71 |
Broker | 13.15 |
Broker | 11.05 |
Broker | 3.12 |
Broker | 8.94 |
Broker | 2.74 |
Broker | 4.07 |
Broker | 5.60 |
Broker | 0.85 |
Broker | 0.28 |
Broker | 16.40 |
Broker | 6.39 |
Broker | 1.90 |
Broker | 9.49 |
Broker | 6.70 |
Broker | 0.19 |
Broker | 12.39 |
Broker | 6.54 |
Broker | 10.92 |
Broker | 2.15 |
Broker | 4.36 |
Broker | 11.07 |
Broker | 9.24 |
Broker | 2.67 |
Broker | 8.97 |
Broker | 1.87 |
Broker | 1.53 |
Broker | 5.23 |
Broker | 6.87 |
Broker | 1.69 |
Broker | 9.43 |
Broker | 8.31 |
Broker | 3.99 |
Broker | 4.44 |
Broker | 8.63 |
Broker | 7.06 |
Broker | 1.57 |
Broker | 8.44 |
Broker | 5.72 |
Broker | 6.95 |