A researcher is conducting a study on the effects of a new teaching method on student performance. She selects a sample of 200 students from a larger population of 2,000 students. Which of the following best illustrates an appropriate use of inferential statistics to draw conclusions about the population?
1
The researcher calculates the mean test scores of the 200 students in the sample and concludes that the mean test score for the entire population of 2,000 students will be the same.
2
The researcher uses the sample mean and standard deviation to construct a 95% confidence interval for the mean test score of the entire population and uses this interval to make informed conclusions.
3
The researcher conducts a descriptive analysis of the sample data and reports the frequency distribution of test scores without making any inferences about the population.
4
The researcher compares the median test scores of the sample and the population directly and updates the population data based on this comparison.