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?
would this be right?
the population parameter of interest is 45%?
the value of the sample statistic is 50%??
To answer these questions, we need to understand the concepts of population parameter and sample statistic.
a. The population parameter of interest is the characteristic of the entire population that you want to estimate or infer. In this case, we are interested in the proportion of voters who will vote for the candidate. The population parameter of interest is the true proportion of all voters in the entire population who will vote for the candidate.
b. A sample statistic is a measure that describes a characteristic of a sample. It is used to estimate the population parameter. In this case, 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.
Now, let's calculate the values:
a. The population parameter of interest is not directly given in the question. However, we can estimate it as the proportion of voters in the entire population who will vote for the candidate. To calculate this, we divide the number of voters who will vote for the candidate by the total number of voters:
Population proportion = Number of voters for the candidate / Total number of voters
= 35 / 150
= 0.2333 (rounded to four decimal places)
So, the estimated population parameter of interest is approximately 0.2333 or 23.33%.
b. The value of the sample statistic is the proportion of voters in the sample who indicate they will vote for the candidate:
Sample proportion = Number of voters for the candidate in the sample / Total number of voters in the sample
= 35 / 150
= 0.2333 (rounded to four decimal places)
Therefore, the value of the sample statistic is also approximately 0.2333 or 23.33%.
Please note that the values are the same for the population parameter and sample statistic in this scenario since we are using the same data. However, in general, the sample statistic may not be exactly the same as the population parameter due to random sampling and other factors.