Question

Suppose you plan to take an SRS from a population of men to determine the mean height for that population. Suppose you know that the standard deviation of the population distribution is ? = 2.8 inches.

1. What would be your margin of error for a 90% level of confidence if you were planning to select 36 men for your sample?

2. What would be your margin of error for a 95% level of confidence if you were planning to select 36 men for your sample?

3. Compare your answers in parts (a) and (b). How does increasing the level of confidence (while maintaining the same sample size) affect the margin of error?

4. What would be your margin of error for a 95% level of confidence if you were planning to select 64 men for your sample?

5. What would be your margin of error for a 95% level of confidence if you were planning to select 100 men for your sample?

6. Compare your answers in parts (b), (d) and (e). Each of these requires the same confidence level but for a different sample size. How does increasing the sample size affect the margin of error?

7. What size sample would you need in order to be 95% confident that your x? will be within ± 0.5 inches of the mean height for the population?

Answer 1

As here population standard deviation is given we will use z distribution to find Margin of Error

1. For 90% CI, z value is 1.645 as

As here population standard deviation is given we will use z distribution to find Margin of Error For 90% CI, z value is 1.645 as P(- 1.645 < z < 1,645) = 0.90 So Margin of Error is = z times sigma/ squareroot n = 1.645 times 2.8/6 = 0.7677 For 95%, z value is 1.96 as (- 1.96 < z < 1.96) = 0.95 So Margin of Error is E = z times sigma/ squareroot n = 1.96 times 2.8/6 = 0.9147 Increasing the level of confidence (while maintaining the same sample size) will increase the margin of error. For n = 64 and CI level of 95% Margin of Error is E = z times sigma/ squareroot n = 1.96 times 2.8/8 = 0.686

So Margin of Error is

2. For 95%, z value is 1.96 as

So Margin of Error is

3.  Increasing the level of confidence (while maintaining the same sample size) will increase the margin of error.

4. For n=64 and CI level of 95%

Margin of Error is