Explain the concept of interpreting a confidence interval for the difference of two means.
If the interval contains 0, there is no significant difference between the two population means. If 0 is not in the interval, there is a significant difference.
Explain the relationship between sample size and the width of a confidence interval.
As sample sizes increase, the width of the confidence interval for the difference of two means tends to decrease, providing a more precise estimate.
Explain the implication of 0 being included in a confidence interval for the difference of two means.
If 0 is included, it suggests that there is no significant difference between the means of the two populations being compared.
Explain the implication of 0 NOT being included in a confidence interval for the difference of two means.
If 0 is not included, it suggests that there is a statistically significant difference between the means of the two populations being compared.
Explain how larger samples lead to better estimates in confidence intervals.
With larger samples, our sample means get closer to the true population means, reducing the standard error and leading to a smaller margin of error.
What is a statistical claim?
A statement about a population, often comparing two populations to see if they are the same or different.
What is the null hypothesis?
The starting assumption that there's no difference between the population means of the two groups being compared.
Define 'confidence interval'.
A range of values, calculated from sample data, that is likely to contain the true value of a population parameter.
Define 'margin of error'.
The range of values above and below the sample statistic in a confidence interval. It quantifies the uncertainty in estimating a population parameter.
What does a narrow confidence interval indicate?
A more precise estimate of the population parameter, typically resulting from a larger sample size.
What are the differences between interpreting a confidence interval that includes 0 and one that does not?
Includes 0: No significant difference between means | Does not include 0: Significant difference between means
What are the differences between a wide and a narrow confidence interval?
Wide: Less precise estimate, often due to smaller sample size | Narrow: More precise estimate, often due to larger sample size
What are the differences between interpreting a 90% and a 95% confidence interval?
90%: Less confidence that the interval contains the true difference in means | 95%: More confidence that the interval contains the true difference in means
