Suppose There Are Two Candidates, Ie Jones And Johns I

Suppose That There Are Two 2 Candidates Ie Jones And Johns In T

Suppose that there are two (2) candidates (i.e., Jones and Johns) in the upcoming presidential election. Sara notes that she has discussed the presidential election candidates with 15 friends, and 10 said that they are voting for candidate Jones. Sara is therefore convinced that candidate Jones will win the election because Jones gets more than 50% of votes.

Answer the following questions in the space provided below: 1. Based on what you now know about statistical inference, is Sara’s conclusion a logical conclusion? Why or why not? 2. How many friend samples Sara should have in order to draw the conclusion with 95% confidence interval? Why? 3. How would you explain your conclusion to Sara without using any statistical jargon? Why?

Paper For Above instruction

Statistical inference is a fundamental aspect of understanding and interpreting data collected from samples to make broader conclusions about populations. In Sarah's case, her conclusion that Jones will win the election because more than half of her 15 friends support him requires scrutiny through the lens of statistical inference principles. While her observations might seem convincing given that 10 out of 15 friends support Jones, this sample size is relatively small, and conclusions drawn from such a limited sample may not reliably reflect the opinions of the larger voter population. This introduces the risk of sampling bias and reduced confidence in the generalizability of her conclusion.

From a statistical perspective, Sara's conclusion is not entirely logical or reliable because it is based on a small, non-representative sample. To make a confident prediction with a 95% confidence interval — meaning she can be 95% sure her conclusion reflects the true support level in the entire population — she would need a larger, randomly selected sample of voters. Typically, the sample size required can be estimated using sample size calculation formulas, which depend on the expected proportion of support and the desired confidence level. For example, assuming she expects similar support proportions and wants a margin of error of about 10%, she might need to survey at least 35-50 people. If she desires a smaller margin of error, the sample size must increase accordingly. Using the formula for estimating sample size for proportions: n = (Z^2 p (1 - p)) / E^2, where Z is the Z-score for 95% confidence (~1.96), p is the estimated proportion support, and E is the margin of error, Sara can determine the minimum number of respondents needed for a reliable conclusion.

Explaining this to Sara without statistical jargon involves emphasizing the importance of having a bigger and more diverse group of friends to truly understand who will win. Just because a small number of her friends support Jones doesn't guarantee that Jones will win the election overall, because her friends might not represent the broader population's opinions. To be more confident about the prediction, she needs to ask more people, so the result is more balanced and reliable. A larger, more representative sample reduces guesswork and helps her see the real trend of voter support rather than relying on a small, possibly biased group.

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