Mat 510 Homework Assignment 9 Due Soon

Mat 510 Homework Assignment homework Assignment 9 due in week 10 and W

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

The scenario presented involves Sara's informal judgment about the likely winner of an upcoming presidential election based on her small sample of friends' opinions. From the standpoint of statistical inference, Sara's conclusion that Jones will win solely because more than half of her 15 friends favor him is not entirely logical or reliable. This is because a sample size of only 15 friends is too small to confidently predict the outcome of a national election, which involves a vastly larger population.

Statistical inference revolves around using data from a sample to make generalizations about a population. When Sara states that Jones will win because 10 out of her 15 friends support him, she is making a conclusion based on a very limited and possibly unrepresentative sample. The small sample size raises concerns about sampling variability; different groups of just 15 people could yield different results. Therefore, her conclusion lacks statistical validity because it does not account for the larger population’s diversity and the potential for sampling error.

To determine how many friends Sara should survey to confidently assert with a 95% confidence level that Jones will win, we need to consider the margin of error and the population proportion. Using standard sample size formulas for proportions, assuming the worst-case scenario (where our estimate's variability is highest at 50%), the sample size required for a 95% confidence level and a ±5% margin of error is approximately 385 respondents. This size ensures that the estimate of support for Jones would be within a 5 percentage point range with 95% confidence. This larger sample size minimizes the effects of randomness and allows for more reliable generalizations about the overall voting intention of the population.

Explaining this to Sara without statistical jargon involves emphasizing the importance of sampling size. I would tell her that just asking 15 friends is like trying to predict the result of a huge event — like a national election — by listening to only a tiny fraction of the crowd. To be really sure about what the whole population thinks, she needs to ask more people. The more people she surveys, the more confident she can be about her prediction, because larger samples tend to better represent the diverse opinions of everyone involved. This approach ensures her conclusion is based on a more accurate reflection of the larger group's preferences, much like how polling organizations conduct extensive surveys to forecast election results reliably.

References

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