Question

1. A study reports that the mean birth weight of 81 term full-term infants is 6.1 lbs. The study also reports a SE of 0.22 lbs.

a. What is the margin of error of this estimate for 95% confidence? [2 points]

b. What is the 95% confidence interval for u ? [2 points]

2. A researcher assumes that the standard deviation of the weekly sugar consumption in children in the community is 100g.

a. How large a sample is needed to estimate mean sugar consumption in the community with a margin of error of 10g at 95% confidence? [2 points]

b. How many children should be studied if the researcher is willing to accept a margin of error of 25 at 95% confidence? [2 points]

3. The calcium content content values in a sample of n=5 teeth (% calcium) are 33.4, 36.2, 34.8, 35.2, 35.5.

a. Provide a 99% confidence interval for u . [2 points]

Answer 1

1)a) For 95% confidence interval the critical value is z^* = 1.96

Margin of error (E) = z^* * SE

                           = 1.96 * 0.22

                           = 0.4312

b) The 95% confidence interval for is

+/- E

= 6.1 +/- 0.4312

= 5.6688, 6.5312

2) For 95% confidence interval the critical value is z^* = 1.96

Margin of error = 10

b) Margin of error = 25

3) = (33.4 + 36.2 + 34.8 + 35.2 + 35.5)/5 = 35.02

s = sqrt(((33.4 - 35.02)^2 + (36.2 - 35.02)^2 + (34.8 - 35.02)^2 + (35.2 - 35.02)^2 + (35.5 - 35.02)^2)/4) = 1.04

df = 5 - 1 = 4

For 99% confidence interval, the critical value is t^* = 4.61

The 99% confidence interval for is

= 35.02 +/- 2.14

= 32.88, 37.16