Homework Assignment 9 Due In Week 10 And Worth 30 Poi 350393

Sheet1homework Assignment 9due In Week 10 And Worth 30 Pointssuppose 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 20 friends, and 12 said that they are voting for candidate Jones. Sara is therefore convinced that candidate Jones will win the election because Jones gets more than 25% 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

In evaluating Sara’s conclusion about the upcoming presidential election, applying principles of statistical inference reveals that her reasoning may not be entirely sound. Sara's assumption that because 12 out of 20 friends favor Jones implies Jones will win is a classic example of overgeneralization from a small, non-random sample. Statistical inference requires sampling random and sufficiently large populations to make reliable predictions regarding a larger population — in this case, the entire electorate.

Firstly, Sara’s sample size of 20 friends is quite small. Such a limited sample is unlikely to accurately reflect the voting intentions of the entire voting population. Many factors such as sampling bias, non-response bias, or variation among different demographic groups could distort the results. Moreover, the sample may not be representative if her friends are not demographically diverse or if there are underlying biases influencing their choices. Therefore, her conclusion that Jones will win because he exceeds a particular percentage threshold (25%) is not logically justified based solely on her small, convenience sample.

To make a more reliable prediction with 95% confidence, Sara should increase her sample size significantly. The exact number of friends she needs to interview can be calculated using the margin of error formula associated with confidence intervals for proportions. Assuming a proportion close to 0.6 (because 12 out of 20 favor Jones), and aiming for a margin of error of less than ±5%, the sample size required would be approximately 385 respondents. This larger sample would reduce the sampling variability and increase the confidence that her estimate truly reflects the population's voting intention.

Explaining this to Sara without statistical jargon can involve using everyday language: The smaller your group, the less certain you can be about what they believe or will do. To be more confident that your guess about who will win is correct, you need to ask more friends or more people in general. Think of it like trying to guess a big crowd’s favorite ice cream flavor — the more people you ask, the more accurate your guess will be. So, if she wants her prediction to be trustworthy, she needs to talk to a larger, more diverse group of people.

In conclusion, Sara’s current sample is too small to confidently predict the election outcome. Increasing the sample size is essential to achieving a statistically valid and confident forecast, aligning her prediction more closely with the actual voting behavior of the larger population.

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