Question

Statistics Question

Data provided below

(To be done with EVIEWS or any other data processor)

d)

e) 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.

(f) 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.

(g) Perform the other tests mentioned in part (e). 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.

(h) Compare your answers in parts (f) and (g) 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

Answer 1

(e) Here we can perform the Wilcoxon's signed-rank test as we do not have any distributional assumption. The test should be one-sided as to check the population central location is larger than 5%.

(f) The null hypothesis is true central location is equal to 5 against the alternative hypothesis is that is greater than 5.

Here the p-value is less than 0.05 so we reject the null hypothesis and conclude on the basis of the given data that the central location is greater than 5%.

We can perform Shapiro Wilk test to check the validity of the normality assumption.

here the p-value is less than 0.05, so reject the null and conclude that the normality assumption does not hold true.

(g) Here we conduct t-test

, where is the population mean.

here the null hypothesis is also rejected at 5% level of significance and conclude that the population mean is significantly greater than 5.

(h) In both cases, we have seen that the null hypothesis is rejected at 5% level of significance but the assumption of normality is failed. So it is better to perform the nonparametric test (Wilcoxon sign-ranked test) than the parametric test (t-test) where the distribution of the given data is not specified. Again one point to be said that we assume the distribution to be symmetric in nonparametric setup. hence, it is useful.