A fitness trainer uses maximal oxygen uptake (VO2max, ml/kg/min) as a measure of cardiovascular health. They have developed a new training program and have recruited 30 females aged 30-39 to train with them. They measure VO2max prior to training and at the conclusion of the program 12 weeks later. Has the VO2max changed?

A full analysis is required with

Justification of approach [2]

null/alternative hypothesis [4]

visualisation [3]

description of the visualisation (location, spread, shape) [1]

assumptions [6]

is this analysis valid? [1]

analysis in R/Excel [2]

interpretation (including a confidence interval) [5]].

	VO2max_before	VO2max_after	difference
1	29.19762	33.32994	4.132321
2	30.84911	31.37376	0.524643
3	39.79354	46.26917	6.475628
4	32.35254	38.74321	6.390667
5	32.64644	38.75434	6.107905
6	40.57532	46.01853	5.443201
7	34.30458	39.07417	4.769588
8	25.67469	27.36514	1.690441
9	28.56574	29.03592	0.470187
10	29.77169	29.86934	0.097645
11	38.12041	36.64687	-1.47353
12	33.79907	34.75948	0.960414
13	34.00386	29.67688	-4.32698
14	32.55341	45.39819	12.84478
15	29.22079	37.2606	8.03981
16	40.93457	37.31902	-3.61554
17	34.48925	34.47483	-0.01442
18	22.16691	21.83364	-0.33328
19	35.50678	41.40661	5.899826
20	29.63604	31.2192	1.583155
21	26.66088	29.92747	3.266593
22	30.91013	32.76739	1.857266
23	26.86998	28.65563	1.785648
24	28.35554	37.19856	8.843011
25	28.8748	29.74595	0.871145
26	23.56653	33.14889	9.582353
27	36.18894	30.44517	-5.74376
28	32.76687	37.68993	4.923069
29	26.30932	28.92859	2.619271
30	38.26907	41.34878	3.079708