QQuestionStatistics
QuestionStatistics
What is the critical value t
∗
for a 90% confidence interval when n= 15?
A. 1.645
B. 1.753
C. 1.761
D. 1.960
12 months agoReport content
Answer
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Step 1:I'll solve this step-by-step using statistical hypothesis testing principles:
Step 2:: Identify the Key Information
- We need to find the critical t-value ($$t^{*}$$)
- Confidence level = 90% - Sample size (n) = 15
Step 3:: Determine Degrees of Freedom
- Degrees of freedom (df) = $$n - 1
- df = 15 - 1 = 14
Step 4:: Calculate Significance Level
- For a 90% confidence interval, the significance level $$\alpha = 1 - 0.90 = 0.10
- This means we need the t-value with \alpha/ 2 = 0.05 in each tail
Step 5:: Consult t-Distribution Table
- The critical t-value is $$t^{*} = 1.761
- For 14 degrees of freedom and a two-tailed test at 90% confidence
Step 6:: Verify the Options
- Comparing the given choices, $$1.761$$ corresponds to option C
Final Answer
Key Insights: - The critical t-value depends on both confidence level and degrees of freedom - For a 90% confidence interval with 15 samples, the critical value is 1.761 - This value is used to construct confidence intervals or conduct hypothesis tests
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