Question

In an election, suppose that of voters support the incumbent candidate. convert all proportions to decimal format. if we poll of these voters at random, the probability distribution for the proportion of the polled voters that support the incumbent candidate can be modeled by the normal distibution pictured below. complete the boxes accurate to two decimal places . note: the left box is standard errors below the population proportion. the middle box is the population proportion. and, the right box is standard errors above the population proportion.

a. True
b. False

Answer 1

The population proportion supporting a candidate in an election can be estimated using normal distribution given a large sample size, with the confidence interval determined by the sample proportion, sample size, and desired level of confidence.

Step-by-step explanation:

In the context of an election, determining the population proportion that supports a particular candidate is a classic problem in statistics, specifically within the subset of descriptive statistics. To estimate the population proportion, categorical data is collected via polls, which often results in a yes or no outcome (e.g., support or do not support a candidate).

The problem suggests that when we sample a fraction of the population, say 'p' (in decimal), the sample's proportion supporting the incumbent candidate can be modeled by a normal distribution if certain conditions are met. Essentially, when we have a large sample size, the sample proportion 'P prime' will distribute normally with mean 'p' (population proportion) and standard deviation sqrt(p*q/n), where q = 1-p. For a confidence interval, we take the sample proportion and add or subtract the error bound, which is calculated as Z * standard deviation of the sampling distribution, where Z is the Z-score associated with the desired level of confidence.

To construct a confidence interval for the population proportion who believe the president is doing an acceptable job, we would apply the formula for the error bound, find the sample proportion (P'), calculate the standard error (SE) using P'(1-P')/n, where n is the sample size, and then apply the formula P' ± (Z * SE) for the confidence interval. A 90% confidence interval will have a corresponding Z-score that determines the range within which we believe the true population proportion lies.