In a study, the reported distances of two small groups of randomly selected GPS units are measured. The difference in sample means (μ₠âˆ' μ₂) is âˆ'0.12 miles. A t-test of the hypothesis Hâ‚€: μ₠= μ₂ versus Ha: μ₠≠ μ₂ is set up. The test statistic is âˆ'2.84, and the critical values are âˆ'2.228 and 2.228. What is the appropriate conclusion?
Reject H0 based on evidence that the mean reported distance difference is not 0 miles.
The test statistic of -2.84 falls outside the critical values of -2.228 and 2.228, indicating that there is sufficient evidence to reject the null hypothesis (H0) in favor of the alternative hypothesis (Ha). This suggests that the mean difference in reported distances is statistically significant and not equal to zero.
This option accurately reflects the result of the t-test, as the test statistic of -2.84 exceeds the critical value threshold, confirming that the observed difference in means is statistically significant. Thus, this conclusion is warranted based on the provided evidence.
This choice is incorrect because failing to reject the null hypothesis would imply that the observed difference is not statistically significant. The comparison of -0.12 miles to zero does not determine the outcome of the hypothesis test; it is the test statistic that dictates the conclusion.
This option misrepresents the findings of the t-test. The calculated test statistic provides sufficient evidence to conclude that there is a significant difference in means. Therefore, stating insufficient evidence contradicts the statistical analysis performed.
This choice is logically flawed, as rejecting H0 indicates evidence against the hypothesis of equal means. If the mean difference were equal to zero, we would fail to reject H0, not reject it.
The t-test results demonstrate that the null hypothesis can be rejected, indicating that the mean reported distance difference is statistically significant and not equal to zero. This conclusion is supported by the test statistic exceeding critical values, affirming that the evidence favors the alternative hypothesis of a significant difference in means.
Related Questions
View allA researcher has a list of all the students in a school district. The...
A regression analysis was performed... The regression equation is y =...
Consider the four normal distributions shown. What is the distribution...
A student is conducting research on the study habits of fellow student...
A researcher splits participants in an experiment into four randomly s...
Related Quizzes
View all0PC1 Planning Instructional Strategies for Meaningful Learning Version 1
AP01 Elementary Literacy Curriculum Version 1
AQ01 Applied Healthcare Statistics C784 Version 1
BJ01 Introduction to Business Finance Version 1
C172 Network and Security Foundations Version 1
C180 Introduction to Psychology Version 1
C180 Introduction to Psychology Version 2
CKC1 Introduction to Humanities Version 1
DZ01 Mathematics for Elementary Educators III MATH 1330 Version 1
FF01 Human Growth and Development Version 1
- ✓ 500+ Practice Questions
- ✓ Detailed Explanations
- ✓ Progress Analytics
- ✓ Exam Simulations