Analyzing the investment returns of technology firms is your job as an intern at a venture capital firm. Over the previous five years, the company has invested in fifty-five different IT firms. A dataset showing the yearly return on investment is provided to you.(ROI) as a percentage for every new business. The data shows a broad spectrum of outcomes, from very successful endeavors to underperforming ones.

Refer to the data set provided below

Assume that all tests' assumptions are met unless otherwise indicated.

a) Plot the variable "Returns" as a histogram. Describe if the returns have a normal distribution or not.

b)Assume you select a basic random sample of five businesses, each of whose returns are as follows: 3.05, 1.05, 5.2, 1.09, and 2.21. Compute and interpret a 95% confidence interval on the average return of startups that the venture capital firm has invested in using the genuine population standard deviation. Show your manual calculations and provide a Excel output confirming your results. (Manual calculations and Excel)

c)Given this sample, what is the highest degree of confidence at which you can draw a confidence interval that excludes 0? (HINT: What is the lowest z-value at which the sample mean is not exceeded by the margin of error?)

d)Verify that the sample selected in subsection (b) fits every requirement needed for a confidence interval.

e)We can evaluate the average return of the startups to make sure the venture capital business is profitable. The binary variable "Positive" in the dataset determines whether or not each startup produced a return larger than 0%. Perform a hypothesis test to see if there is a chance that a startup will have a positive return larger than 0.5 using Excel. At a significance level of 5%, apply the p-value and critical value approaches. Incorporate each phase of the hypothesis testing process, including hypotheses, decision rule, p-value, and conclusion. Show Excel output forverification.

f)Using both the information from the confidence interval obtained in part b) and the hypothesis test obtained in part e), what can you say about the profitability of the startups?

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