A candidate for a political office claims that he will win the election. A poll is conducted, and 35 of 150 voters indicate that they will vote for the candidate, 100 voters indicate that they will vote for his opponent, and 15 voters are undecided.
a. What is the population parameter of interest?
b. What is the value of the sample statistic that might be used to estimate the population parameter?
c. Would you tend to believe the candidate based on the results of the poll?
a. The population parameter of interest in this case would be the proportion of voters in the entire population who will vote for the candidate.
b. The value of the sample statistic that might be used to estimate the population parameter is the proportion of voters in the sample who indicate they will vote for the candidate.
c. To determine whether to believe the candidate based on the results of the poll, we need to calculate the estimated proportion of voters who will vote for the candidate based on the sample and compare it to the proportion claimed by the candidate.
To calculate the estimated proportion of voters who will vote for the candidate, divide the number of voters who indicated they will vote for the candidate (35) by the total number of voters (150):
Estimated Proportion = Number of voters who will vote for the candidate / Total number of voters
= 35 / 150
= 0.2333 (rounded to four decimal places)
The estimated proportion of voters who will vote for the candidate based on the sample is approximately 0.2333.
To compare this to the proportion claimed by the candidate, we need to know the exact proportion claimed. If the proportion claimed by the candidate is greater than 0.2333, it would suggest that the candidate may indeed win the election based on the results of the poll. However, if the proportion claimed by the candidate is lower, it would cast doubt on the candidate's claim and suggest that the candidate's chances of winning may be lower than expected.