Math Problem Statement
Solution
To solve this hypothesis test, we will:
1. Identify the hypotheses:
- Null hypothesis (): Car crash fatalities occur with equal frequency on all days of the week.
- Alternative hypothesis (): Car crash fatalities do not occur with equal frequency on all days of the week.
2. Perform the Chi-Square Goodness-of-Fit Test:
We are given the observed frequencies of fatalities for each day, and we assume that the expected frequencies would be equal if is true. To calculate the test statistic (), we need: Where:
- : Observed frequency
- : Expected frequency
Observed Frequencies ():
- Sun: 129
- Mon: 110
- Tues: 103
- Wed: 100
- Thurs: 107
- Fri: 137
- Sat: 163
Expected Frequency ():
Assuming equal frequencies, the expected frequency for each day is:
3. Calculate the Chi-Square Test Statistic ():
We calculate for each day and sum these values:
4. Determine the p-value:
The degrees of freedom () for this test is:
Using the chi-square distribution table or calculator, we compare the test statistic with the critical value for and , or we calculate the p-value directly.
5. Conclusion:
- If the p-value is less than 0.05, reject , meaning there is sufficient evidence to suggest that fatalities do not occur with equal frequency.
- If the p-value is greater than 0.05, fail to reject , meaning there is insufficient evidence to suggest a difference.
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Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
Chi-Square Goodness-of-Fit Test
Probability and Statistics
Formulas
Chi-Square Statistic: χ² = Σ((O - E)² / E)
Degrees of Freedom: df = Number of Categories - 1
Theorems
Chi-Square Distribution
Suitable Grade Level
College/University Statistics
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