As a research assistant in an economic research institute, you are embarking on a study focused on the performance metrics of small and medium enterprises (SMEs) in the renewable energy sector. The research has gathered data from 55 SMEs over a span of ten years. This collected data illustrates the annual growth rates, presenting a spectrum of results ranging from significant expansion to noticeable declines. Unless specified otherwise, assume that the conditions for all statistical tests have been satisfied. The dataset is shown after the question. Provide either manual calculations or statistical software output. Question: In order to understand whether SMEs in the renewable energy sector are predominantly experiencing growth, it's essential to examine the average growth rate. The dataset includes a binary variable 'GrowthPositive' which indicates whether each SME's growth rate is above 0. Conduct a hypothesis test to see if the probability of an SME having a positive growth rate surpasses 0.5. Apply a 5% significance level and thoroughly detail every phase of the hypothesis testing (including hypothesis statements, decision rule, p-value calculation, and a concluding statement with its rationale).

Annual Growth Rate	GrowthPositive
-1.78	0
-1.63	0
-1.13	0
-1.1	0
-1.09	0
-0.82	0
-0.79	0
-0.65	0
-0.58	0
-0.41	0
-0.39	0
-0.33	0
-0.2	0
-0.09	0
0.09	1
0.73	1
0.8	1
0.9	1
1.05	1
1.09	1
1.24	1
1.31	1
1.37	1
1.54	1
1.58	1
1.58	1
1.59	1
1.6	1
2.01	1
2.21	1
2.27	1
2.37	1
2.39	1
2.42	1
2.48	1
2.59	1
2.62	1
2.71	1
2.75	1
2.81	1
2.89	1
2.94	1
3.05	1
3.35	1
3.41	1
3.74	1
3.86	1
3.89	1
4.26	1
5.2	1
5.24	1
5.54	1
5.65	1
7.03	1
9.76	1