Question

The daily intake of calcium was measured (in milligrams) from a random sample of 16 women between the ages of 20 and 29. The sample mean and sample standard deviation of the observed data were calculated to be 866.8 and 255.5, respectively. (4 decimals places)

1. Conduct a 95% confidence interval for the population mean daily intake of calcium. State the lower bound.

2. Conduct a 95% confidence interval for the population mean daily intake of calcium. State the upper bound.

3. What is the margin of error for the above confidence interval

Answer 1

Solution :

Given that,

= 866.8

s = 255.5

n = 16

Degrees of freedom = df = n - 1 = 16 - 1 = 15

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,15 = 2.131

Margin of error = E = t_/2,df * (s /n)

= 2.131 * (255.5 / 16)

= 136.1176

The 95% confidence interval estimate of the population mean is,

- E < < + E

866.8 - 136.1176 < < 866.8 + 136.1176

730.6824 < < 1002.9176

1) Lower bound = 730.6824

2) Upper bound = 1002.9176

3) Margin of error = E = 136.1176