To determine if the model is significantly different from the experimental probability for choosing a red car in the various schools, we first gather the relevant data and then perform a Chi-square test. Based on the provided results, we will identify the significant schools.
Here's the data given for each school:
- East Bank High:
- Red cars: 19
- Total cars: 86
- South High:
- Red cars: 11
- Total cars: 47
- Mountain View High:
- Red cars: 4
- Total cars: 42
- Day Spring High:
- Red cars: 18
- Total cars: 110
- Hinckley High:
- Red cars: 33
- Total cars: 144
First, calculate the overall totals from all schools:
- Total number of red cars observed: [tex]\( 19 + 11 + 4 + 18 + 33 = 85 \)[/tex]
- Total number of cars observed: [tex]\( 86 + 47 + 42 + 110 + 144 = 429 \)[/tex]
Next, we find the expected number of red cars for each school using the ratio of total red cars to total cars:
- Expected number of red cars at East Bank High: [tex]\( \frac{85}{429} \times 86 \approx 17.04 \)[/tex]
- Expected number of red cars at South High: [tex]\( \frac{85}{429} \times 47 \approx 9.31 \)[/tex]
- Expected number of red cars at Mountain View High: [tex]\( \frac{85}{429} \times 42 \approx 8.32 \)[/tex]
- Expected number of red cars at Day Spring High: [tex]\( \frac{85}{429} \times 110 \approx 21.79 \)[/tex]
- Expected number of red cars at Hinckley High: [tex]\( \frac{85}{429} \times 144 \approx 28.53 \)[/tex]
Perform the Chi-square goodness of fit test:
- Chi-square test statistic: 4.136
- p-value: 0.388
A p-value of 0.388 indicates that there is no significant difference between the observed and the expected number of red cars in any of the schools, as the p-value is much higher than 0.05.
Thus, none of the schools show a statistically significant difference from the experimental probability for choosing a red car. Therefore, based on the data and chi-square test results, none of the schools should be selected as having a model significantly different from the experimental probability.
