Discuss the concept of degrees of freedom in the context of t-tests and their significance for making accurate statistical inferences

Discuss the concept of degrees of freedom in the context of t-tests and their significance for making accurate statistical inferences. How do degrees of freedom differ between z-tests and t-tests?
In recent news, there has been debate about the effects of screen time on children’s cognitive development. Choose a specific cognitive outcome measure (e.g., attention, memory, executive function) and write a research question for a one-sample t-test study to investigate whether the average score of a group on that measure differs significantly from a well-established normative population means. Be sure to specify the:
Dependent variable
Relevant population (Sample)
Predetermined value (which can be hypothetical)
Complete the following readings from your textbook, Essentials of Statistics for the Behavioral Sciences:
Chapter 8: Introduction to Hypothesis Testing
Chapter 9: Introduction to the t Statistic
ANSWER
Degrees of freedom in t-tests and their significance for making accurate statistical inferences
In statistical hypothesis testing, degrees of freedom (df) represent the number of independent values that can vary in the calculation of a statistic. In the context of t-tests, degrees of freedom are crucial for determining the t-distribution and making accurate statistical inferences about the population mean.
The degrees of freedom for a t-test depend on the sample size (n) and whether the population variance (σ²) is known or estimated. When the population variance is known, the degrees of freedom are simply n-1. However, in most cases, the population variance is unknown, and the sample variance (s²) is used as an estimate. In this case, the degrees of freedom for a t-test are n-2.
The degrees of freedom directly influence the shape of the t-distribution, which is used to determine the p-value and assess statistical significance. As the degrees of freedom increase, the t-distribution approaches the standard normal distribution, making it more likely to observe extreme t-values.
In summary, degrees of freedom are essential for understanding the behavior of the t-distribution and making accurate statistical inferences about the population mean. They reflect the variability in the data and determine the p-value associated with a particular t-statistic.
Research question for a one-sample t-test study on screen time and attention
In recent years, concerns have been raised about the potential negative effects of screen time on children’s cognitive development, particularly attention. To investigate whether screen time is associated with attention deficits, a one-sample t-test study could be conducted.
The research question for this study would be:
“Does the average attention score of a group of children with high screen time differ significantly from the well-established normative population mean for attention?”
Specifics of the study
Dependent variable: Attention score
Relevant population (sample): Children with high screen time
Predetermined value: The well-established normative population mean for attention
By comparing the average attention score of the sample group to the established normative mean, the study aims to determine whether there is a statistically significant difference between the two groups. A significant difference would suggest that high screen time is associated with attention deficits.