Question

A research program used a representative random sample of men and women to gauge the size of the personal network of older adults. Each adult in the sample was asked to "please name the people you have frequent contact with and who are also important to you." The responses of 2,817 adults in this sample yielded statistics on network size, that is, the mean number of people named per person was x- 14.8, with a standard deviation of s 9.9. Complete parts a through d.

a. Give a point estimate for μ. (Type an integer or a decimal.)

b. Give an interval estimate for μ. Use a confidence interval of 0.95.

Answer 1

a) The point estimate for the population mean is the sample mean hence point estimate = 14.8

b)

The formula for estimation is:

μ = M ± Z(sM)

where:

M = sample mean, here used M instead of X(bar)
Z = Z statistic determined by confidence level
sM = standard error = √(s2/n)

Hence ,

M = 14.8
Z= 1.96 at 95 % confidence level
sM = √(9.92/2817) = 0.19

μ = M ± Z(sM)
μ = 14.8 ± 1.96*0.19
μ = 14.8 ± 0.366

We can be 95% confident that the population mean (μ) falls between 14.434 and 15.166.