Confidence Intervals and Sampling Methods

The video is a review session on confidence intervals, covering three main scenarios: using proportions, means with known sigma, and means with unknown sigma. It explains the conditions to check for each scenario, such as randomness, independence, and normality. The video also details the calculations involved and how to conclude in context. Finally, it reviews multiple choice questions to reinforce understanding.

Which of the following scenarios involves using a t-distribution?

• Proportions

• Means with known sigma

• Means with unknown sigma

• None of the above

What is a necessary condition for a sample to be considered random?

• The sample must be normally distributed

• The sample size must be greater than 30

• Each observation must be independent

• The sample must be less than 10% of the population

For a confidence interval using proportions, what is the normality check?

• Sample size must be greater than 30

• n * p and n * (1-p) must be greater than or equal to 10

• The sample must be normally distributed

• The sample must be random

When calculating a confidence interval for means with known sigma, what is the critical value used?

• Z star

• T star

• P hat

• X bar

What should you always include when concluding a statistical analysis?

• The exact value of the mean

• The confidence interval in context

• The standard deviation

• The sample size

Which factor will decrease the margin of error in a confidence interval?

• Increasing the confidence level

• Decreasing the sample size

• Decreasing the standard deviation

• None of the above

If a 90% confidence interval is calculated from 100 samples, approximately how many intervals will contain the true mean?

• 100

• 90

• 50

• 0

In an experiment with two groups of 200 men, what effect does increasing the sample size to 1000 men have?

• Increases precision

• No change in precision

• Decreases precision

• Increases bias

What is the effect of a larger sample size on the margin of error?

• Increases the margin of error

• Decreases the margin of error

• No effect on the margin of error

• Depends on the confidence level

Which statement is true about the probability of the true mean being within a confidence interval?

• It depends on the sample size

• It is either 0 or 1

• It is always 50%

• It is always 90%