A college Statistics class conducted a survey concerning community attitudes about the college's large homecoming celebration. T
hat survey drew its sample in the following manner: Telephone numbers were generated at random by selecting one of the local telephone exchanges (first three digits) at random and then generating a random four-digit number to follow the exchange. If a person answered the phone and the call was to a residence, then that person was taken to be the subject for interview. (Undergraduate students and those under voting age were excluded, as was anyone who could not speak English.) Calls were placed until a sample of 200 eligible respondents had been reached. Required:
a. Did every telephone number that could occur in that community have an equal chance of being generated?
b. Did this method of generating telephone numbers result in a simple random sample (SRS) of local residences? Explain.
c. Did this method generate an SRS of local voters? Explain.
d. Is this method unbiased in generating samples of households? Explain.
A) Yes, every telephone number that could occur in that community will have an equal chance of being generated because the telephone numbers were generated randomly.
B) No, this method of generating telephone numbers would not result in a simple random sample (SRS) of local residences because the first three digits were generated in a different random way than the last four digits.
C) No, this method would not generate an SRS of local voters because not everybody will be pick up when they call because they may not be at home or they may be too busy to pick up.
D) No, this method is not unbiased in generating samples of households because there will be nonresponse bias since not everyone will pick up the call
If I'm not mistaken, the 76 degrees means that a is equal to 76 deg. Just visually, if you were to widen that angle, similarly, a would grow just as much.
