Confidence Intervals for Population Proportion quiz #1 Flashcards
Confidence Intervals for Population Proportion quiz #1
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What type of variable is required to construct a confidence interval for a population proportion? A categorical variable with two possible outcomes (success or failure) is required to construct a confidence interval for a population proportion. What is the formula for the point estimate p̂ when constructing a confidence interval for a population proportion? The point estimate p̂ is calculated by dividing the number of successes x by the sample size n. This gives p̂ = x/n. How do you determine if the sampling distribution of p̂ is approximately normal? Check that both np and nq are greater than or equal to 5, where n is the sample size and p and q are the proportions of success and failure. This ensures at least 5 successes and 5 failures. What does the critical z-value zα/2 depend on when constructing a confidence interval for a proportion? The critical z-value zα/2 depends on the chosen confidence level for the interval. It can be found using a z-table or calculator. How do you calculate the margin of error for a confidence interval for a population proportion? The margin of error E is calculated as zα/2 times the square root of p̂(1-p̂)/n. This quantifies the uncertainty around the point estimate. What should you do if the calculated sample size n is a decimal when determining the minimum sample size for a desired margin of error? You should round up to the next whole number because you cannot sample a fraction of a subject. This ensures the margin of error requirement is met. What value of p̂ should you use when calculating minimum sample size if p̂ is not provided? Use p̂ = 0.5 when it is not given, as this yields the largest required sample size for a given margin of error. This is a conservative approach. Which function on the TI-84 calculator is used to construct a confidence interval for a population proportion? The '1-PropZInterval' function is used on the TI-84 calculator. It quickly calculates the confidence interval after entering sample data. How do you interpret the bounds of a confidence interval for a population proportion? The bounds indicate the range in which you are confident the true population proportion lies. For example, a 90% interval means you are 90% confident the true proportion is between the lower and upper bounds. What steps are involved in using a TI-84 calculator to find a confidence interval for a population proportion? First, access the test menu and select the 1-PropZInterval function, then enter the sample data and confidence level. Finally, calculate to view the interval bounds.