Confidence Intervals and Sample Size

The video tutorial explains confidence intervals for population proportions and how to calculate the required sample size to achieve a specific margin of error. It provides an example using household computer ownership data and demonstrates how to adjust the margin of error. The tutorial covers equations for sample size calculation with and without prior estimates and includes problem-solving examples.

What is the primary purpose of a confidence interval?

• To determine the exact value of a population parameter

• To calculate the mean of a sample

• To find the median of a dataset

• To provide a range of values within which a population parameter is likely to fall

What does a confidence interval consist of?

• A point estimate and a mode

• A point estimate and a variance

• A point estimate and a margin of error

• A point estimate and a standard deviation

In the example given, what was the point estimate for the proportion of households with at least one computer?

• 0.80

• 0.76

• 0.70

• 0.85

What was the original margin of error in the example provided?

• 0.070

• 0.100

• 0.059

• 0.030

What is the desired margin of error in the example when recalculating the sample size?

• 0.050

• 0.040

• 0.020

• 0.030

Which value is used for z in a 95% confidence interval?

• 2.58

• 1.64

• 2.33

• 1.96

What is the significance of using 1.96 in the calculation?

• It represents a 90% confidence interval

• It represents a 95% confidence interval

• It represents a 99% confidence interval

• It represents a 100% confidence interval

If you have a prior estimate of the population proportion, which equation should you use?

• The second equation

• The first equation

• The third equation

• The fourth equation

How many people are needed in the sample if the prior estimate of the population proportion is known?

• 900

• 500

• 600

• 779

How many people are needed in the sample if there is no prior estimate of the population proportion?

• 1000

• 1200

• 1500

• 1680