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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?
Case context: A health psychologist wants to test if university students accurately estimate the calories of a chocolate chip cookie that contains 250 calories. He collects data from a sample of students, yielding a sample mean () of calories and a standard deviation () of . He calculates a score of . Suppose he decides to switch his analysis from a two-tailed test (critical value of ) to a one-tailed test because prior literature suggests students tend to underestimate calories. Apply this scenario to evaluate the statistical consequences of this change.
Question: 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?
Sample answer: Changing to a one-tailed test shifts the critical value from to a less severe threshold of . This lower threshold makes it easier to reject the null hypothesis because the rejection region is larger in the predicted direction. Since the calculated score of is still more extreme than , the researcher rejects the null hypothesis and concludes that students significantly underestimate the cookie's calories.
Key points:
- The one-tailed critical value is , which is closer to zero than .
- A less severe critical value makes it easier to reject the null hypothesis when results trend in the predicted direction.
- The calculated score of is more extreme than , leading to a rejection of the null hypothesis.
Rubric: The response must identify the new critical value of , explain that it makes rejecting the null hypothesis easier due to a less severe threshold in the predicted direction, and state that the null hypothesis is rejected to conclude students significantly underestimate calories.
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Research Methods in Psychology - 4th American Edition @ KPU
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