Question

What are the three pieces of information needed to determine the margin of error?

Identify the three ways that you can minimize the margin of error ?

Constructr a 90% two sided confidence interval around the true value of When the sample data used are: 45, 37, 65, 39, 46, 60, 45, 44, 48, 51, 55 , 62

How large of a sample size, n, do you need to be 90% confident that your margin error is no more than 2 points, when the population standard deviation is sigma = 35)

Answer 1

What are the three pieces of information needed to determine the margin of error?

The three pieces of information needed to determine the margin of error are given as critical value, standard deviation, and sample size.

Identify the three ways that you can minimize the margin of error?

If we increase the sample size, the margin of error decreases.

If we decrease the critical value or confidence level, the margin of error decreases.

If we reduce the standard deviation, the margin of error decreases.

Construct a 90% two sided confidence interval around the true value of When the sample data used are: 45, 37, 65, 39, 46, 60, 45, 44, 48, 51, 55 , 62

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 49.75

S = 8.996211324

n = 12

df = n – 1 = 11

Confidence level = 90%

Critical t value = 1.7959

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 49.75 ± 1.7959*8.996211324/sqrt(12)

Confidence interval = 49.75 ±4.6639

Lower limit = 49.75 -4.6639 =45.09

Upper limit = 49.75 +4.6639 = 54.41

Confidence interval = (45.09, 54.41)

How large of a sample size, n, do you need to be 90% confident that your margin error is no more than 2 points, when the population standard deviation is sigma = 35)

The sample size formula is given as below:

n = (Z*σ/E)^2

We are given

σ = 35

Confidence level = 90%

Critical Z value = 1.6449

(by using z-table)

Margin of error = E = 2

The sample size is given as below:

n = (Z*σ/E)^2

n = (1.6449*35/2)^2

n = 828.6194

Required sample size = 829