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 is the proportion of voters 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 who indicate they will vote for the candidate in the sample.

c. Based on the results of the poll, it is difficult to make a definitive conclusion about whether the candidate will win the election. The proportion of voters in the sample who indicate they will vote for the candidate is 35 out of 150, which is approximately 0.2333 or 23.33%. However, it is important to note that this is just a sample and may not accurately represent the entire population of voters. Additionally, there are still 15 voters who are undecided and may change their preference before the election. Therefore, further analysis and information would be needed to determine if the candidate is likely to win.

a. The population parameter of interest is the proportion of voters 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 that they will vote for the candidate. In this case, it would be calculated as the number of voters who will vote for the candidate divided by the total number of voters in the sample. So, in this case, the sample proportion would be 35/150 = 0.2333 (or 23.33%).

c. Based on the results of the poll, it might be difficult to believe the candidate will win the election. The sample proportion (23.33%) is lower than the proportion of voters who indicate they will vote for the opponent (100/150 = 0.6667 or 66.67%). Additionally, there are still 15 voters who are undecided, and their vote could go either way. Therefore, it would be prudent to be cautious in accepting the candidate's claim based solely on the results of this poll. It is important to remember that a sample is only an estimate of the population, and there can be sampling errors or other factors that influence the actual outcome of an election.