A city council of a small city wants to know the proportion of eligible voters that oppose having a incinerator of Phoenix garbage opened just outside of the city limits. They randomly select 100 residential numbers from the city’s telephone book that contains 3,000 such numbers. Each selected residence is then called and asked for (a) The total number of eligible voters and (b) the number of voters opposed to the incinerator. A total of 157 voters were surveyed; of these, 23 refused to answer the question. Of the remaining 134 voters, 112 opposed the incinerator, so the council estimates the proportion by
Ṕ = 112/134 = .83582
With
Ṽ (Ṕ) = .83582(1 − .83582)/134 = 0.00102.
Are these estimates valid? Why, or why not?