In sociology, a personal network is defined as the people with whom you make frequent contact. A research program used a stratified random sample of men and women born between 1908 and 1937 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. Based on the number of people named, the personal network size for each adult was determined. The responses of 2,826 adults in this sample yielded statistics on network size that is, the mean number of people named person was 14.7, with a standard deviation of 10.3 Complete parts a through b.

a) Form a 95% confidence interval for the mean personal network size of all older adults. (Round to the nearest hundredths as needed)

Answer: ( ), ( )

b) Give a practical interpretation of the interval found in part (a).

(Round to the nearest hundredths as needed)

Answer: ( ), ( )