Given the Following Null and Alternative Hypotheses H₀ : μ₁

question 86

Multiple Choice

Given the following null and alternative hypotheses H₀ : μ₁ ≥ μ₂
H_A : μ₁ < μ₂
Together with the following sample information
Assuming that the populations are normally distributed with equal variances,test at the 0.05 level of significance whether you would reject the null hypothesis based on the sample information.Use the test statistic approach.

• A)Because the calculated value of t = -2.145 is less than the critical value of t = -1.6973,reject the null hypothesis.Based on these sample data,at the α = 0.05 level of significance there is sufficient evidence to conclude that the mean for population 1 is less than the mean for population 2.
• B)Because the calculated value of t = -1.814 is less than the critical value of t = -1.6973,reject the null hypothesis.Based on these sample data,at the α = 0.05 level of significance there is sufficient evidence to conclude that the mean for population 1 is less than the mean for population 2.
• C)Because the calculated value of t = -1.329 is not less than the critical value of t = -1.6973,do not reject the null hypothesis.Based on these sample data,at the α = 0.05 level of significance there is not sufficient evidence to conclude that the mean for population 1 is less than the mean for population 2.
• D)Because the calculated value of t = -1.415 is not less than the critical value of t = -1.6973,do not reject the null hypothesis.Based on these sample data,at the α = 0.05 level of significance there is not sufficient evidence to conclude that the mean for population 1 is less than the mean for population 2.

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Definitions:

Cognitive Errors

Cognitive errors refer to systematic flaws or biases in human reasoning and perception that can lead to incorrect judgments, decisions, or interpretations.

Counterfactual Thinking

The psychological process of imagining alternative outcomes to events that have already occurred, often starting with "if only" scenarios.

Affective Forecasting

The ability to predict one’s emotional reactions to future events

Psychologists

professionals who study the human mind and behavior, offering insights and interventions for mental and emotional well-being.