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Example of a One-Sample t-Test
To demonstrate a one-sample -test, imagine a health psychologist investigating whether university students accurately estimate the calories in a chocolate chip cookie. The null hypothesis () assumes accurate estimation. The researcher asks a sample of students, resulting in a sample mean () of calories and a standard deviation () of . Plugging these statistics into the one-sample -test formula yields a score of . For a two-tailed test with degrees of freedom, the critical value is . Because the calculated score is more extreme than this critical value, the researcher rejects the null hypothesis and concludes that students significantly underestimate the cookie's calories. If the researcher had a strong theoretical reason to expect an underestimation, a one-tailed test with a less severe critical value of could have been used, making it easier to reject the null hypothesis if the results trended in the expected direction.
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Research Methods in Psychology - 4th American Edition @ KPU
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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 -test to compare the mean stress scores of a sample of emergency room nurses () to the known general population average (). Despite obtaining a statistically significant result () due to a large sample size, the researcher evaluates the finding as having low practical importance because the calculated _____ was only , indicating a negligible magnitude of difference.
Based on the definition of a one-sample -test, which statistical values are compared in this procedure?
In a one-sample -test, the alternative hypothesis is formulated as , 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 -test.
Analyze the structural relationship between the sample mean (), the hypothetical population mean (), and the competing hypotheses in a one-sample -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 -test, what specific standard of comparison is the single sample mean evaluated against, and how is the null hypothesis mathematically defined?
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In the cookie-calorie one-sample -test example, what is the two-tailed critical value for degrees of freedom at the .05 significance level?
In the cookie-calorie study, switching from a two-tailed to a one-tailed test makes it easier to reject the null hypothesis when results trend in the predicted direction, because the one-tailed critical value () is less extreme than the two-tailed critical value ().
Match each element from the cookie-calorie one-sample -test study to the role it plays in the statistical decision-making process.
In the health psychologist's cookie-calorie study, because the sample mean estimate of is lower than the null hypothesis value of and the calculated score is more extreme than the critical value, the researcher rejects the null hypothesis and concludes that students significantly _____ the cookie's calories.
Order the following steps in evaluating the results of the cookie-calorie one-sample -test, from formulating the initial hypothesis to making the final scientific decision.
In the health psychologist's cookie-calorie example, what was the specific null hypothesis () value representing accurate estimation?
In the context of the cookie-calorie estimation study, explain the role of the null hypothesis () and describe how the researcher uses the calculated score of and the critical value of to make a statistical decision about student estimation accuracy.
Based on the case context, if the researcher changes the analysis to a one-tailed test with a critical value of , how does this modify the critical value threshold, how does it affect the ease of rejecting the null hypothesis, and what is the final conclusion regarding the students' estimations?
Analyze the relationship between the sample size () and the degrees of freedom () in this one-sample -test. How would an increase in sample size affect the degrees of freedom and the critical value needed to reject the null hypothesis?