Voting Survey In a survey of 1002 people, 70% said that they voted in a recent presidential election (based on data from ICR Research Group). Voting records show that 61% of eligible voters actually did vote.

b. Find a 95% confidence interval estimate of the percentage of people who say that they voted.

Verified step by step guidance

Step 1: Identify the sample proportion (p̂) and sample size (n). The sample proportion is the percentage of people who said they voted, which is 70% or 0.70. The sample size is 1002.

Step 2: Determine the critical value (z*) for a 95% confidence level. For a 95% confidence interval, the critical value z* is approximately 1.96 (this value corresponds to the standard normal distribution).

Step 3: Calculate the standard error (SE) of the sample proportion using the formula: SE = sqrt((p̂ * (1 - p̂)) / n). Substitute p̂ = 0.70 and n = 1002 into the formula.

Step 4: Compute the margin of error (ME) using the formula: ME = z* × SE. Use the critical value z* = 1.96 and the standard error calculated in Step 3.

Step 5: Construct the confidence interval by adding and subtracting the margin of error from the sample proportion. The confidence interval is given by: [p̂ - ME, p̂ + ME].

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Confidence Interval

A confidence interval is a range of values, derived from sample statistics, that is likely to contain the true population parameter with a specified level of confidence, typically 95%. It provides an estimate of uncertainty around a sample statistic, allowing researchers to infer about the population from which the sample was drawn.

Sample Proportion

The sample proportion is the ratio of the number of individuals in a sample who have a particular characteristic to the total number of individuals in that sample. In this case, it refers to the percentage of survey respondents who claimed they voted, which is essential for calculating the confidence interval.

Margin of Error

The margin of error quantifies the uncertainty in the estimate of a population parameter based on a sample. It is calculated using the standard error of the sample proportion and reflects how much the sample proportion might differ from the true population proportion, influencing the width of the confidence interval.

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