Math Problem Statement
Solution
From the image provided, we are working on a hypothesis test with the following details:
Hypotheses:
- Null hypothesis
- Alternative hypothesis
Information provided:
- Test statistic (rounded to 3 decimal places)
- -value = 0.192 (rounded to 3 decimal places)
- Level of significance
Steps to complete the hypothesis test:
-
Determine one-tailed or two-tailed test:
- Since , this is a one-tailed test.
-
Input the test statistic:
- Test statistic .
-
Shade the area representing the -value:
- For , the area to the right represents the -value (since this is a one-tailed test).
-
Input the -value:
- .
Decision Rule:
- If , reject .
- If , fail to reject .
Here, is greater than . Hence, we fail to reject . This means there is not enough evidence to support the claim that at the 0.10 level of significance.
Would you like further explanation or assistance with any specific step?
5 Questions for Expansion:
- What is the relationship between -value and significance level ?
- How is the test statistic calculated in hypothesis testing?
- What are the assumptions required for conducting a -test for the mean?
- How would the decision change if were 0.05 instead of 0.10?
- Can you explain why this test is one-tailed rather than two-tailed?
Tip:
Always visualize the problem on a normal distribution curve to better understand the area represented by the -value, especially for one-tailed and two-tailed tests.
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Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
One-Tailed Test
Significance Level
p-value
Formulas
Test statistic (z) = (sample mean - population mean) / (standard error)
Decision Rule: Reject H0 if p-value <= alpha
Theorems
Central Limit Theorem: Ensures the sampling distribution of the mean is approximately normal.
p-value Method for Hypothesis Testing
Suitable Grade Level
Grades 11-12 or College Level (Statistics)
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