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Explain how an increase in sample size generally affects the margin of error in a confidence interval, assuming all other factors remain constant.
Explain how an increase in sample size generally affects the margin of error in a confidence interval, assuming all other factors remain constant.
Increasing the sample size reduces the margin of error because it provides a more precise estimate of the population parameter.
Describe a scenario where using a t-distribution is more appropriate than using a z-distribution when constructing a confidence interval for a population mean.
Describe a scenario where using a t-distribution is more appropriate than using a z-distribution when constructing a confidence interval for a population mean.
A t-distribution is more appropriate when the population standard deviation is unknown and the sample size is small (typically less than 30).
A researcher wants to determine if there's a statistically significant difference in average test scores between two different teaching methods. Describe the null and alternative hypotheses in this scenario.
A researcher wants to determine if there's a statistically significant difference in average test scores between two different teaching methods. Describe the null and alternative hypotheses in this scenario.
Null hypothesis: There is no difference in average test scores between the two teaching methods. Alternative hypothesis: There is a difference in average test scores between the two teaching methods.
Explain the concept of 'Type II error' in hypothesis testing. What is its practical implication?
Explain the concept of 'Type II error' in hypothesis testing. What is its practical implication?
Given a scatterplot showing a strong negative linear relationship between two variables, what can you say about the correlation coefficient, r?
Given a scatterplot showing a strong negative linear relationship between two variables, what can you say about the correlation coefficient, r?
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