Using significance level = 0.05 and the sample data provided, test if the mean 2019 log return for stocks trading on the Frankfurt Stock Exchange is more than 0.045 units higher than the mean for 2020. Write down the hypotheses, the test statistic, the test decision (with reason) and conclusion

	index	lr2019	lr2020
1	FTSE	0.152198	0.023106
2	FTSE	0.106496	-0.06684
3	FTSE	0.052306	0.099872
4	FTSE	0.094568	0.047562
5	FTSE	0.068402	0.196239
6	FTSE	0.168689	0.153569
7	FTSE	0.104371	-0.05976
8	FTSE	0.112353	-0.01647
9	FTSE	0.116404	0.001021
10	FTSE	0.047293	-0.10975
11	FTSE	0.162882	0.100458
12	FTSE	0.089893	-0.06276
13	FTSE	0.076809	-0.08803
14	FTSE	0.207695	-0.04701
15	FTSE	0.043075	-0.18326
16	FTSE	0.145092	-0.01059
17	FTSE	-0.02186	-0.26737
18	FTSE	0.111464	-0.07676
19	FTSE	0.078475	-0.11606
20	FTSE	-0.05965	0.073003
21	FTSE	0.103984	-0.09068
22	FTSE	-0.17916	-0.28247
23	FTSE	0.019567	-0.03306
24	FTSE	0.058978	-0.14197
25	FTSE	0.154793	0.001638
26	FTSE	0.166979	0.002278
27	FTSE	0.03856	0.110011
28	FTSE	0.038779	-0.10168
29	FTSE	0.058836	-0.04613
30	FTSE	0.117891	0.107871
31	FTSE	0.126986	0.036695
32	FTSE	0.158739	0.214345
33	FTSE	0.285222	-0.00687
34	FTSE	-0.12818	0.246571
35	FTSE	-0.0927	-0.00436
36	FTSE	0.07664	-0.12242
37	FTSE	0.190701	0.063473
38	FTSE	0.019744	-0.10341
39	FTSE	-0.05627	-0.15612
40	FTSE	-0.03859	-0.19378
41	FTSE	0.089613	-0.0455
42	FTSE	-0.10442	-0.08536
43	FTSE	0.133502	-0.19341
44	FTSE	0.004892	-0.5923
45	FTSE	0.086063	-0.01541
46	FTSE	0.380356	0.011565
47	FTSE	0.029539	-0.09183
48	FTSE	0.019442	0.095547
49	FTSE	0.090163	-0.1671
50	FTSE	0.117831	-0.05623
51	FTSE	0.081131	-0.2343
52	FTSE	0.280562	0.065327
53	FTSE	0.165946	-0.12985
54	FTSE	0.035467	-0.01318
55	FTSE	0.091903	-0.03809
56	FTSE	0.044896	-0.15635
57	FTSE	0.245132	0.004188
58	FTSE	0.209243	0.252396
59	FTSE	-0.16825	0.028625
60	FTSE	0.145001	0.01145
61	FTSE	0.01432	-0.0317
62	FTSE	0.008298	0.028321
63	FTSE	0.071433	-0.02655
64	FTSE	0.128211	0.051131
65	FTSE	0.16608	0.011632
66	FTSE	0.081793	0.084485
67	FTSE	-0.08453	-0.78825
68	FTSE	0.095318	-0.10956
69	FTSE	-0.06171	-0.00839
70	FTSE	0.135042	0.000391
71	FTSE	0.183069	0.023736
72	FTSE	0.141542	-0.04089
73	FTSE	-0.01386	-0.23607
74	FTSE	0.108451	-0.01099
75	FTSE	0.092301	-0.04972
76	FTSE	0.097503	-0.08407
77	FTSE	0.153717	0.103984
78	FTSE	0.123883	0.018181
79	FTSE	0.067893	-0.18443
80	FTSE	0.091168	-0.01172
81	FTSE	0.15212	-0.06687
82	FTSE	0.127899	-0.04252
83	FTSE	0.024856	0.004123
84	FTSE	0.1077	-0.02287
85	FTSE	0.194035	-0.08125
86	FTSE	-0.0178	-0.08404
87	FTSE	0.065558	0.119911
88	FTSE	0.024613	-0.19402
89	FTSE	0.100283	-0.12487