Question
In an election there are two candidates. Being a statistician, you are interested in predicting the result of the election. So, you plan to conduct a survey. Using the learning skill of this course answer the following question. How many people should be surveyed to be at least 95% sure that the estimate is within 0.05 of the true value?
Answer :
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Skip in 10
In order to determine how many people should be surveyed to estimate the proportion of votes for a candidate with a specified level of accuracy and confidence, it is essential to apply the principles of sampling theory and probability distributions. The situation described involves estimating a population proportion, which is the fraction of voters who support a particular candidate. Since it is usually impractical to survey the entire population, a sample is taken, and the sample proportion is used as an estimate of the true population proportion. The fundamental idea behind this problem is based on the sampling distribution of the sample proportion. When a sufficiently large random sample is drawn from a population, the sample proportion follows an approximately normal distribution due to the Central Limit Theorem. This approximation allows us to construct confidence intervals around the sample proportion and determine how close the estimate is likely to be to the true population value. The requirement is to be at least 95% confident that the estimate is within 0.05 of the true proportion. This means we are constructing a confidence interval with a margin
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Related Questions
Explain the procedure of assigning probability in the discrete world of probability theory.
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In an election there are two candidates. Being a statistician, you are interested in predicting the result of the election. So, you plan to conduct a survey. Using the learning skill of this course answer the following question. How many people should be surveyed to be at least 95% sure that the estimate is within 0.05 of the true value?
a) Suppose two friends Anjali and Prabhat trying to meet for a date to have lunch say between 1 pm to 2 pm. Suppose they follow the following rules for this meeting:
Each of them will arrive either on time or 10 minutes late or 20 minutes late or 30 minutes late or 40 minutes late or 50 minutes late or 1 hour late. All these arrival times are equally likely for both of them.
Whoever of them reaches first will wait for the other to meet only for 10 minutes. If within 10 minutes the other does not reach, he/she leaves the place and they will not meet.
Find the probability of their meeting.