solved I’m working on a data analytics question and need an

I’m working on a data analytics question and need an explanation to help me learn.

1.Explain why it is important to calculate a confidence interval.
2.Explain the meaning of the term “95% confidence.”
3.For a fixed level of confidence, what happens to a confidence interval for µ when we increase the sample size?
4.Suppose that for a sample size of n=100, we find that the sample mean is 50. Assuming that the standard deviation = 2, calculate the confidence intervals for the population mean µ with the following confidence levels.
a.90%
b.92%
c.95%
d.97%
e.99%
5.Explain how the standard deviation of the t curve changes as the number of degrees of freedom describing a t curve increases.
For a fixed sample size, what happens to a confidence interval for ? when we increase the level of confidence?
It gets?
Item 4
In each of the following cases, compute 95 percent, 98 percent, and 99 percent confidence intervals for the population proportion p.
 
(a)pˆp^ = .1 and n = 113 (Round your answers to 3 decimal places.)
 
(b)pˆp^ = .5 and n = 256. (Round your answers to 3 decimal places.)
(c)pˆp^ = .8 and n = 116. (Round your answers to 3 decimal places.)
(d) pˆp^ = .2 and n = 53. (Round your answers to 3 decimal places.)
In each of the following cases, determine whether the sample size n is large enough to use the large sample formula to compute a confidence interval for p.
(a)  pˆp^= .1, n = 30
n(p-hat) =
n(1-(p-hat) =
(b)  pˆp^= .1, n = 100
n(p-hat) =
n(1-(p-hat) =
(c)  pˆp^= .5, n = 50
n(p-hat) =
n(1-(p-hat) =
(d)  pˆp^= .8, n = 400
n(p-hat) =
n(1-(p-hat) =
(e)  pˆp^= .9, n = 30
n(p-hat) =
n(1-(p-hat) =
(f)  pˆp^= .99, n = 200
n(p-hat) =
n(1-(p-hat) =