9231 FPS · Notes & worked examples
Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.
Recall
Maths4U Original · Short practice
A null model assigns equal probabilities to four outcomes, with no fitted parameters. Observed counts are \(36,28,40,24\).
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the expected frequency in each category.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
A null model assigns equal probabilities to four outcomes, with no fitted parameters. Observed counts are \(38,28,43,23\).
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the expected frequency in each category.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Method
Maths4U Original · Short practice
A null model assigns equal probabilities to four outcomes, with no fitted parameters. Observed counts are \(38,28,43,23\).
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the chi-squared statistic.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
A null model assigns equal probabilities to four outcomes, with no fitted parameters. Observed counts are \(40,28,46,22\).
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the chi-squared statistic.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Apply
Maths4U Original · Short practice
A null model assigns equal probabilities to four outcomes, with no fitted parameters. Observed counts are \(40,28,46,22\).
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the p-value.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
A null model assigns equal probabilities to four outcomes, with no fitted parameters. Observed counts are \(37,33,39,31\).
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the p-value.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Check understanding
Maths4U Original · Short practice
A null model assigns equal probabilities to four outcomes, with no fitted parameters. Observed counts are \(37,33,39,31\).
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
For a separate fit with \(\displaystyle k=8\) retained classes and one estimated parameter, find the degrees of freedom.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
A null model assigns equal probabilities to four outcomes, with no fitted parameters. Observed counts are \(39,33,42,30\).
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
For a separate fit with \(\displaystyle k=5\) retained classes and one estimated parameter, find the degrees of freedom.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.