MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Transcribed Image Text:**Educational Content: Median Household Income Hypothesis Testing**
**Context:**
In a particular county, the median household income is $46,250. A researcher is interested in determining whether the students at a local community college have a median household income significantly lower than the county's median. She selects a random sample of 15 students and finds the following distribution:
- 12 students have a household income below the county median.
- 1 student has an income equal to the county median.
- 2 students have a household income above the county median.
The researcher conducts a hypothesis test using a significance level of 0.05. The question is: **What is the decision rule for this test?**
**Multiple Choice:**
1. **Option A:** Reject \( H_0 \) if the number above the median is \( \leq 3 \) or \( \geq 8 \).
2. **Option B:** Reject \( H_0 \) if the number above the median is \( \leq 3 \).
3. **Option C:** Reject \( H_0 \) if the number above the median is \( \leq 2 \) or \( \geq 10 \).
4. **Option D:** Reject \( H_0 \) if the number above the median is \( \leq 2 \).
In this context, \( H_0 \) represents the null hypothesis that there is no difference between the median incomes of the college students and the county overall. The decision rule will guide whether this hypothesis should be rejected based on the sample data and set significance level.
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