while the sample size is large, the statement "We can assume that the majority of all auto workers favor a strike since the number sampled is large and those in favor of a strike are over 50%." lacks sufficient data to be confirmed as true. Therefore, the correct answer would be:
B. False.
The statement in question is making an inference about the population of auto workers based on the sample results. To evaluate whether the statement is likely to be true or false, we need to consider a few key points related to statistical inference:
1. Sample Size: A sample size of 2,845 is fairly large, which generally allows for more confident inferences about the population, assuming the sample is representative.
2. Representativeness: For the inference to be valid, the sample needs to be representative of the entire population of auto workers. This means it needs to be randomly selected and free from biases that could skew the results.
3. Margin of Error and Confidence Level: Even with a large sample size, there is always a margin of error in the estimates from sample data. Without knowing the exact percentage that favored the strike and the confidence level (often 95% or 99% in polling data), we cannot make a definitive statement.
4. Over 50%: The statement that "over 50% of those in the sample declared they would strike" indicates a majority, but without the exact percentage and the margin of error, it's not possible to state with certainty that the majority of all auto workers favor a strike.
5. Statistical Significance: To claim that the majority of all auto workers favor a strike, the percentage favoring the strike in the sample must be statistically significantly greater than 50%, factoring in the margin of error.
Without additional information on how much over 50% the sample was, the margin of error, or the confidence level, we can't mathematically calculate the certainty of the inference.
Based on these points, while the sample size is large, the statement "We can assume that the majority of all auto workers favor a strike since the number sampled is large and those in favor of a strike are over 50%." lacks sufficient data to be confirmed as true. Therefore, the correct answer would be:
B. False.