(Data below) (to be done with EVIEWS or any data processor)
Millions of investors buy mutual funds, choosing from thousandsof possibilities. Some funds can be purchased directly from banksor other financial institutions (direct) whereas others must bepurchased through brokers (broker), who charge a fee for thisservice. A group of researchers randomly sampled 50 annual returnsfrom mutual funds that can be acquired directly and 50 from mutualfunds that are bought through brokers and recorded their net annualreturns (NAR, %), which are the returns on investment afterdeducting all relevant fees.1
(a) In general, we can conduct hypothesis tests on a populationcentral location with EViews by performing the (one sample) t-test,the sign test or the Wilcoxon signed ranks test.2 Suppose we wouldlike to know whether there is evidence at the 5% level ofsignificance that the population central location of NAR is largerthan 5%. Which test(s) offered by EViews would be the mostappropriate this time? Explain your answer by considering theconditions required by these tests.
(b) Perform the test you selected in part (e) abovewith EViews. Do not forget to specify the null and alternativehypotheses, to identify the test statistic, to make a statisticaldecision based on the p-value, and to draw an appropriateconclusion. If the test relies on normal approximation, alsodiscuss whether this approximation is reasonable this time.
(c) Perform the other tests mentioned in part (a). Again, do notforget to specify the null and alternative hypotheses, to identifythe test statistics, to make statistical decisions based on thep-values, and to draw appropriate conclusions. Also, if the testsrely on normal approximation, discuss whether these approximationsare 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 returnsis normally, or at least symmetrically distributed or not? Explainyour 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 |
