In sociology, a personal network is defined as the people with whom you make frequent contact. The Living Arrangements and Social Networks of Older Adults (LSN) 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 (e.g., in your neighborhood) 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 2,819 adults in the LSN sample yielded the following statistics on network size: = 14.6; s = 9.8.
a. Give a point estimate for the mean personal network size of all older adults.
b. Form a 95% confidence interval for the mean personal network size of all older adults.
c. Give a practical interpretation of the interval you found in part b.
d. Give the conditions required for the interval in part b to be valid.