please use r studio

This assignment must be submitted as a single PDF file, see "One Small PDF" in the Resources section of LMS for information on making a PDF. Please practice making such a PDF well before assignment submission. Data (VOmaxFemales.csv) is in the Data Files section on LMS Visualisations should be publication quality (title, labels, etc) Those using R are not required to provide code unless it is essential to understanding the answer provided

1. [24 marks] 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]].

2. [4 marks] A group of elite athletes were assigned to one of two groups: primarily animal protein and primarily plant protein. All meals and snacks were provided for a period of 4 weeks. At the end of the 4 weeks the athletes did some tests including the ability to lift weights as measured by recording their maximum weight lifted in a single repetition. Should this scenario be analysed with a paired t-test or independent sample t-test/regression with a categorical variable with two levels?

this is the data

	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