In: Statistics and Probability
1) The Gallup Poll asked a random sample of 1785 adults whether they attended church or synagogue during the past week. Of the respondents, 44% said they did attend. Suppose that 40% of the adult population actually went to church or synagogue last week. Let p^ be the proportion of people in the sample who attended church or synagogue. Find the probability of obtaining a sample of 1785 adults in which 44% or more say they attended church or synagogue last week. Do you have any doubts about the result of this poll?
2) Suppose 47% of all adult women think they do not get enough time to themselves. An opinion poll interviews 1025 randomly selected women and records the sample proportion who feels they don’t get enough time for themselves. If this sample were repeated numerous times, in what range would the middle 95% of the sample results fall? What is the probability the poll gets a sample in which fewer than 45% say they do not get enough time for themselves?