Question (statistics) (Data below) (to be done with EVIEWS)

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 These data are saved in the twocolumns of the a1.xlsx spreadsheet labelled as Purchase and NAR,respectively. Import these data to EViews.

(a) Are Purchase and NAR qualitative or quantitativevariables? If they are qualitative, are they ranked or unranked? Ifthey are quantitative, are they discrete or continuous? What aretheir levels of measurement? Explain your answers.

(b) Use EViews to obtain the basic descriptivestatistics for NAR. Briefly describe what they tell you about thenet annual returns from mutual funds.

(c) Using the relevant statistics from part (b),estimate with 90% confidence the mean net annual returns. Whatassumption do you have to make to perform this task?

(d) Using the relevant statistics from part (b),briefly evaluate whether the assumption needed for the confidenceinterval in (c) is likely violated.

(e) In general, we can conduct hypothesis tests on apopulation central location with EViews by performing the (onesample) t-test, the sign test or the Wilcoxon signed ranks test.2Suppose we would like to know whether there is evidence at the 5%level of significance that the population central location of NARis larger than 5%. Depending on your answer in part (d), whichtest(s) offered by EViews would be the most appropriate this time?Explain your answer by considering the conditions required by thesetests.

(f) 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.

(g) Perform the other tests mentioned in part (e).Again, do not forget to specify the null and alternativehypotheses, to identify the test statistics, to make statisticaldecisions based on the p-values, and to draw appropriateconclusions. Also, if the tests rely on normal approximation,discuss whether these approximations are reasonable this time.

(h) Compare your answers in parts (f) and (g) to eachother. Does it matter in this case whether the population of netreturns is normally, or at least symmetrically distributed or not?Explain your answer.

Data

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