Question

Please Conduct a Paired Difference Test (use α=5%) for the two data sets below. Thanks.

2012          2015

15.88           20.99
15.54           21.08
16.17           21.15
15.80           21.28
15.99           21.29
16.28           21.31
15.91           21.35
15.77           21.36
15.80           21.36
15.95           21.37
15.86           21.38
16.07           21.39
15.96           21.40
16.20           21.40
15.90           21.41
15.90           21.42
15.96           21.42
16.29           21.44
15.97          21.48
15.95          21.49
16.02          21.49
16.08          21.52
16.01          21.53
16.18          21.54
15.88          21.58
16.14          21.58
15.72          21.64
15.93          21.64
15.69         21.67
16.24         21.69
15.79         21.71
15.69         21.72
16.46         21.72
15.87         21.73
15.80         21.76
15.94         21.79
16.36         21.81
15.90         21.84
15.91         21.84
15.91         21.86
16.07         21.92
16.52         21.93
15.86         21.97
16.07         21.97
15.75         21.99
16.07         22.03
16.04         22.06
16.15         22.13
16.39         22.17
15.87         22.19
15.93         22.29

Answer 1

Null hypothesis :

Alternate hypothesis :  

d : Difference in data ie 2015-2012

Sample Mean of differences

Sample Standard deviation

n : sample size = 51

2012	2015	d: 2015-2012	d-	(d-)2
15.88	20.99	5.11	-0.53	0.28194
15.54	21.08	5.54	-0.10	0.010197
16.17	21.15	4.98	-0.66	0.436895
15.8	21.28	5.48	-0.16	0.025915
15.99	21.29	5.30	-0.34	0.116268
16.28	21.31	5.03	-0.61	0.373297
15.91	21.35	5.44	-0.20	0.040393
15.77	21.36	5.59	-0.05	0.002599
15.8	21.36	5.56	-0.08	0.006558
15.95	21.37	5.42	-0.22	0.048832
15.86	21.38	5.52	-0.12	0.014636
16.07	21.39	5.32	-0.32	0.103028
15.96	21.40	5.44	-0.20	0.040393
16.2	21.40	5.20	-0.44	0.194464
15.9	21.41	5.51	-0.13	0.017156
15.9	21.42	5.52	-0.12	0.014636
15.96	21.42	5.46	-0.18	0.032754
16.29	21.44	5.15	-0.49	0.241062
15.97	21.48	5.51	-0.13	0.017156
15.95	21.49	5.54	-0.10	0.010197
16.02	21.49	5.47	-0.17	0.029234
16.08	21.52	5.44	-0.20	0.040393
16.01	21.53	5.52	-0.12	0.014636
16.18	21.54	5.36	-0.28	0.07895
15.88	21.58	5.70	0.06	0.003483
16.14	21.58	5.44	-0.20	0.040393
15.72	21.64	5.92	0.28	0.077852
15.93	21.64	5.71	0.07	0.004764
15.69	21.67	5.98	0.34	0.114934
16.24	21.69	5.45	-0.19	0.036474
15.79	21.71	5.92	0.28	0.077852
15.69	21.72	6.03	0.39	0.151336
16.46	21.72	5.26	-0.38	0.145146
15.87	21.73	5.86	0.22	0.04797
15.8	21.76	5.96	0.32	0.101774
15.94	21.79	5.85	0.21	0.043689
16.36	21.81	5.45	-0.19	0.036474
15.9	21.84	5.94	0.30	0.089413
15.91	21.84	5.93	0.29	0.083532
15.91	21.86	5.95	0.31	0.095493
16.07	21.92	5.85	0.21	0.043689
16.52	21.93	5.41	-0.23	0.053352
15.86	21.97	6.11	0.47	0.219979
16.07	21.97	5.90	0.26	0.067091
15.75	21.99	6.24	0.60	0.358824
16.07	22.03	5.96	0.32	0.101774
16.04	22.06	6.02	0.38	0.143656
16.15	22.13	5.98	0.34	0.114934
16.39	22.17	5.78	0.14	0.019326
15.87	22.19	6.32	0.68	0.461068
15.93	22.29	6.36	0.72	0.516989
	Total	287.69		5.442851
		5.641

Sample Mean of the differences :	5.641
Sample Standard Deviation of the differences : sd	0.3299
Sample Size : n	51
Level of significance :	5%
Degrees of Freedom : n-1	50

Two Tailed Test:

As P-Value i.e. is less than Level of significance i.e (P-value:0 < 0.05:Level of significance); Reject Null Hypothesis