Answer :
To determine which newspaper's estimate is most likely to be closest to the actual percentage of voters who support the governor for reelection, we need to evaluate the reliability of each estimate. A key factor in the reliability of an estimate derived from a sample is the sample size. Larger sample sizes generally result in more reliable estimates because they tend to reduce the margin of error and provide a more accurate reflection of the population parameter.
Let's analyze the sample sizes provided by each newspaper:
1. The Tribune:
- Sample size [tex]\( n = 1100 \)[/tex] voters
- Sample estimate [tex]\( = 71\% \)[/tex]
2. The Herald:
- Sample size [tex]\( n = 900 \)[/tex] voters
- Sample estimate [tex]\( = 67\% \)[/tex]
3. The Times:
- Sample size [tex]\( n = 700 \)[/tex] voters
- Sample estimate [tex]\( = 81\% \)[/tex]
When comparing the reliability of these estimates, we observe the following:
- The Tribune has the largest sample size, with [tex]\( 1100 \)[/tex] voters. The large sample size makes its estimate of [tex]\( 71\% \)[/tex] the most reliable because it minimizes the margin of error more effectively than the smaller samples.
- The Herald surveyed [tex]\( 900 \)[/tex] voters, which is fewer than The Tribune but more than The Times. Thus, its estimate of [tex]\( 67\% \)[/tex] is reasonably reliable but not as reliable as that of The Tribune.
- The Times has the smallest sample size, with [tex]\( 700 \)[/tex] voters. This means its estimate of [tex]\( 81\% \)[/tex] is likely to have the highest margin of error, making it the least reliable among the three.
Therefore, the estimates can be ranked in terms of reliability based on sample size, with larger sample sizes corresponding to higher reliability. Given that The Tribune surveyed the largest number of voters, its estimate of [tex]\( 71\% \)[/tex] is the most likely to be closest to the actual percentage of voters who support the governor for reelection.
So, the correct answer is:
C. The Tribune, at 71%
Let's analyze the sample sizes provided by each newspaper:
1. The Tribune:
- Sample size [tex]\( n = 1100 \)[/tex] voters
- Sample estimate [tex]\( = 71\% \)[/tex]
2. The Herald:
- Sample size [tex]\( n = 900 \)[/tex] voters
- Sample estimate [tex]\( = 67\% \)[/tex]
3. The Times:
- Sample size [tex]\( n = 700 \)[/tex] voters
- Sample estimate [tex]\( = 81\% \)[/tex]
When comparing the reliability of these estimates, we observe the following:
- The Tribune has the largest sample size, with [tex]\( 1100 \)[/tex] voters. The large sample size makes its estimate of [tex]\( 71\% \)[/tex] the most reliable because it minimizes the margin of error more effectively than the smaller samples.
- The Herald surveyed [tex]\( 900 \)[/tex] voters, which is fewer than The Tribune but more than The Times. Thus, its estimate of [tex]\( 67\% \)[/tex] is reasonably reliable but not as reliable as that of The Tribune.
- The Times has the smallest sample size, with [tex]\( 700 \)[/tex] voters. This means its estimate of [tex]\( 81\% \)[/tex] is likely to have the highest margin of error, making it the least reliable among the three.
Therefore, the estimates can be ranked in terms of reliability based on sample size, with larger sample sizes corresponding to higher reliability. Given that The Tribune surveyed the largest number of voters, its estimate of [tex]\( 71\% \)[/tex] is the most likely to be closest to the actual percentage of voters who support the governor for reelection.
So, the correct answer is:
C. The Tribune, at 71%
