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.

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

In statistical research, what does a hypothetical population mean ($\mu_0$) represent?

In statistical research, a hypothetical population mean ($\mu_0$) is the actual average value calculated directly from the specific data collected in a researcher's sample.

A psychologist investigates whether a new memory technique helps people remember more words than the general population average of 12 words. She tests a group of 30 students and finds they remember an average of 15 words. Match each statistical component to its corresponding value or group in this study.

A social psychologist wants to determine if students at a specific university are more extraverted than the national average score of 3.5. Arrange the steps of the statistical analysis in the correct logical order, starting with the establishment of the theoretical baseline.

You are a lead psychologist designing an original study to determine if a new 'digital-detox' program significantly reduces stress levels in teenagers compared to the average teenager in the general population. Because no recent census data exists for your specific stress scale, you must construct a hypothetical population mean ($\mu_0$) for your hypothesis test. Which of the following research strategies demonstrates the most robust method for synthesizing this $\mu_0$ value?

In statistical research, a(n) _____ population mean ($\mu_0$) represents an expected baseline value for an entire population, against which researchers compare an observed sample mean ($M$) to draw statistical conclusions.

When a psychologist evaluates whether a research sample's average score represents a significant deviation from the population, the hypothetical population mean ($\mu_0$) functions as the specific, interesting _____ of comparison for the study.

A researcher wants to compare the average sleep duration of a sample of college athletes to a known national average sleep duration of 7.2 hours. In this research design, the value 7.2 hours represents the observed sample mean ($M$) of the athletes.

An educational psychologist compares the mean test score of a class using a new curriculum against the historical district mean of 75. Match each statistical component from this study with its correct analytical role or definition.

A researcher wants to evaluate whether a local community's average daily screen time differs from the national baseline of 6.0 hours. Arrange the steps of this statistical evaluation process in the correct logical order, starting with establishing the baseline.