14. The supervisors of a rural county are interested in the proportion of property owners who support the construction of a new high school for the area. Rather than contact all 7,000 of
the owners, the supervisors decide to take a random sample of 300.
(a) During each interview, the supervisor's representative asks, “Do you support the building
of a new high school for the area?” For this sample, 58% of the respondents said yes. If
the representative took a second random sample of 300 property owners, would this
second sample proportion of those who support building a new high school be exactly the
same as that found in the first sample?
(b) If the representative has increased the sample size to 600 owners, what effect would this
have on the estimated proportion of owners who would support building the high school?