Template Statements for Students Writing About Difficult Concepts in Statistics

Template Statements for Students Writing About Difficult Concepts in Statistics

Correct Interpretation of a Confidence Interval

We are 95% [or actual value from the context of the problem if different from 95] confident that the true [population parameter from context of the problem] is between [lower bound estimate] and [upper bound estimate].

Correct Interpretations of a Confidence Level

A 95% [or actual value from the context of the problem if different from 95] confidence level means that if we took repeated simple random samples of the same size, from the [population in the context of the problem], 95% of the intervals constructed using this method would capture the true [population parameter from context of the problem].

Correct Interpretations of a p Value

Assuming that the null hypothesis is true, that [Ho in context of the problem], the p value shows the probability of observing results this large or larger due to sampling error alone.

Assuming that the null hypothesis is true, that [Ho in context of the problem], a p value of [actual p value calculated from the context of the problem] means that we would get a result this extreme or larger [x] times out of 100 due to sampling error alone.

Correct Conclusion Based on a p Value Less than Alpha

Since this p value of [calculated value from the context of the problem] is less than [alpha from the context of the problem], we reject Ho, and conclude that there is sufficient evidence to support the claim that [Ha in the context of the problem].

Correct Conclusion Based on a p Value Greater than Alpha

Since this p value of [calculated value from the context of the problem] is greater than [alpha from the context of the problem], we fail to reject Ho, and conclude that there is not sufficient evidence to support the claim that [Ha in the context of the problem].

Least Square Regression Line

The Least Squares Regression Line is the line that makes the sum of the squared vertical deviations (observed minus expected), as small as possible.

If you have to define observed and expected in the context of the problem:

Observed is defined as [observed y values from the context of the problem] and expected is defined as [y predicted values from the regression line formed using data from the context of the problem].

Coefficient of Determination (r2)

The coefficient of determination shows the percentage of the variation in the [response variable from the context of the problem] that is associated with variation in the [explanatory variable from the context of the problem].