Week 5 Assignment

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 μ 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) =