Question

The editor of a local newspaper wants to publish a prediction of whether or not an amendment will pass. She hires ten pollsters to each ask 100 randomly selected voters if they will vote yes, and it needs at least 60% of the vote to pass. What should the editor include in her prediction?

a. 50% of voters will say yes
b. 55% of voters will say yes
c. 60% of voters will say yes
d. 65% of voters will say yes

Answer 1

The editor should predict the amendment will likely pass since 65% of the voters in a random poll supported it, surpassing the required 60% threshold. For similar assessments, such as mayor approval rates or election polls, statistics and probability guide the interpretations and required sample sizes for accurate predictions.

Step-by-step explanation:

The question regarding whether or not an amendment will pass based on poll results falls within the subject of Mathematics, specifically related to statistics and probability. To make an accurate prediction, the editor should consider the percentage of randomly selected voters who said they would vote 'yes'. If a recent random poll of 50 voters showed that 65% would vote for the amendment, the prediction could lean towards the amendment passing, as it exceeds the required 60% threshold according to that sample.

Review Questions:

1. Most ordinary laws require a '50 percent + 1 vote' majority to pass, making the correct answer d. 50 percent + 1 vote.
2. Without a specific sample size for the mayor's approval study, we cannot provide numerical answers to the questions, but we can say that if there is a 42% approval rate, then 58% disapprove. To find the exact number approved, one would multiply the sample size by 42%. The probability of support during those times is 57% and 60% respectively.
3. In order to estimate the true proportion of college students who voted with 95% confidence and a margin of error no greater than 5 percent, an appropriate sample size must be calculated using a sample size formula for proportions.

Election polls with a 95 percent confidence interval give a range of percentages where pollsters are confident the true value lies within that interval.

A Type I error occurs when we incorrectly conclude the percentage is higher than 60%, whereas a Type II error is the opposite. Increasing the confidence level above 90 percent would typically require a larger sample size to maintain the same margin of error because higher confidence necessitates a larger sample for the same level of precision.