Don't construct a confidence interval: At the end of a television documentary on the nature of government, viewers are invited to tweet an answer to the question, "Do you believe that women are more effective at governing than men are?" A total of 2348 viewers answer the question, and 1247 of them answer "Yes." Explain why these data should not be used to construct a confidence interval for the proportion of people who believe that women are more effective at governing than men are.

Answer:

These are the conditions required for constructing a confidence interval for proportion:

1. The data must be sampled randomly. This should be clearly stated in the problem, but here, it is not stated, so we cannot just presume that the data are sampled randomly
2. The sample values must be independent of each other. Since the date are not sample randomly, we cannot also just assume independence
3. When the sample is drawn without replacement (usually the case), the sample size,n, should be no more than 10% of the population. Since it is not stated here the actual population size, then we are not sure if the given sample size (1500) is not more than 10% of the population
4. The sample size must be sufficiently large. This condition is met (since n > 30)

Question

If the sample is not random, what kind of sample does this represent?

response

If the sample is not random it would be a biased sample meaning some members of the populationhave a lowersampling probability.

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question asking now:

What type of sampling was used?How can you show possible bias with this type of sampling?