Week 4 Confidence interval

What does a 95% confidence interval represent in statistical analysis?

• It contains 95% of the population data

• It indicates a 95% chance that the sample mean is within the interval.

• It includes the true population parameter with 95% probability.

• It excludes 5% of the sample data.

How is the width of a confidence interval affected by increasing the sample size?

• The width decreases

• The width increases.

• The width remains constant.

• The width fluctuates unpredictably.

In a study comparing two treatment groups, a 99% confidence interval for the difference in means ranges from -2 to 6. What can be concluded about the treatment effect?

• There is a significant treatment effect.

• The treatment effect is inconclusive.

• The treatment has no effect.

• The confidence interval is too wide to draw conclusions.

What is the relationship between confidence level and the width of a confidence interval?

• Higher confidence levels result in wider intervals

• Higher confidence levels result in narrower intervals.

• Confidence levels have no impact on interval width

• The relationship depends on the sample size

In a survey, the 95% confidence interval for the mean age of participants is 40 ± 3 years. What does this interval indicate?

• There is a 95% chance that the mean age is exactly 40 years

• The true population mean age is likely between 37 and 43 years.

• The sample mean age is 40 years with 95% certainty.

• The survey results are not reliable

How does increasing the confidence level from 90% to 99% impact the width of a confidence interval?

• The width decreases.

• The width increases.

• The width remains the same.

• The width fluctuates randomly

What does it mean if a confidence interval includes zero when comparing two groups or treatments?

• There is a significant difference between the groups.

• There is no significant difference between the groups.

• The study findings are inconclusive.

• The sample size is too small

Which of the following factors affects the precision of a confidence interval?

• Sample size

• Confidence level

• Population size

• Variability of the data

In a regression analysis, a 95% confidence interval for the coefficient of a predictor variable ranges from 0.2 to 0.8. What does this interval suggest about the predictor's impact?

• The predictor has a significant impact.

• The predictor has no impact

• The predictor's impact is uncertain.

• The sample size is too small to determine impact.

How does the standard deviation of the sample data affect the width of a confidence interval?

• Higher standard deviation leads to narrower intervals.

• Higher standard deviation leads to wider intervals.

• Standard deviation has no impact on interval width.

• The impact of standard deviation depends on the sample size.