Null Hypothesis

Alternative Hypothesis

Assumptions

Formula for the One-Sample t-Test

Dependent-Samples t-Test

Null and Alternative Hypotheses for the One-Sample t-Test

Degrees of Freedom (One-Sample t-Test)

Example of a One-Sample t-Test

What is the primary purpose of a one-sample t-test?

Match each component of the one-sample t-test to its correct description.

A cognitive psychologist is investigating whether the average reaction time of 50 video game players differs from the general population mean of 300 milliseconds. Arrange the following steps of a one-sample t-test in the correct logical order for this study.

A clinical psychologist is conducting a one-sample t-test to compare the average anxiety scores of patients in a new treatment program to a known population mean. If the psychologist observes that the standard deviation within the sample is larger than expected, while the difference between the sample mean and the population mean remains the same, the resulting t-statistic will be closer to zero.

A researcher conducts a one-sample $t$-test to compare the mean stress scores of a sample of emergency room nurses ($M = 42$) to the known general population average ($\mu = 40$). Despite obtaining a statistically significant result ($p < .01$) due to a large sample size, the researcher evaluates the finding as having low practical importance because the calculated _____ was only $0.10$, indicating a negligible magnitude of difference.

Based on the definition of a one-sample $t$-test, which statistical values are compared in this procedure?

In a one-sample $t$-test, the alternative hypothesis is formulated as $\mu \neq \mu_0$, which states that the true population mean differs from the hypothesized value.

A health psychologist is investigating university students' accuracy in estimating the calories in a chocolate chip cookie (which actually has 250 calories). Match each element of this study to its corresponding role in a one-sample $t$-test.

Analyze the structural relationship between the sample mean ($M$), the hypothetical population mean ($\mu_0$), and the competing hypotheses in a one-sample $t$-test. How do these components work together to help researchers evaluate statistical evidence?

Evaluate this research scenario to determine the appropriate statistical test and formulate the precise null and alternative hypotheses. Justify your choice based on the structure of the study.

In the context of a one-sample $t$-test, what specific standard of comparison is the single sample mean evaluated against, and how is the null hypothesis mathematically defined?