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Recall
Exact sign tests — objective 1
Maths4U Original · Short practice
After removing zero differences, 10 independent paired differences contain 9 positive and 1 negative values. The alternative is a positive population median difference.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the expected positive count under \(\displaystyle H_{0}\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Exact sign tests — objective 1
Maths4U Original · Short practice
After removing zero differences, 11 independent paired differences contain 9 positive and 2 negative values. The alternative is a positive population median difference.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the expected positive count under \(\displaystyle H_{0}\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Method
Exact sign tests — objective 2
Maths4U Original · Short practice
After removing zero differences, 11 independent paired differences contain 9 positive and 2 negative values. The alternative is a positive population median difference.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the exact one-sided 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
Exact sign tests — objective 2
Maths4U Original · Short practice
After removing zero differences, 12 independent paired differences contain 9 positive and 3 negative values. The alternative is a positive population median difference.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the exact one-sided p-value.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Apply
Wilcoxon signed-rank tests — objective 3
Maths4U Original · Short practice
Independent paired differences are \(-1,2,3,-4,5,6,7,8,9\). Their absolute values are distinct. Assume a continuous symmetric population of differences and test for a positive shift.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the exact upper-tail p-value for W+.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Wilcoxon signed-rank tests — objective 3
Maths4U Original · Short practice
Independent paired differences are \(-1,-2,3,4,5,6\). Their absolute values are distinct. Assume a continuous symmetric population of differences and test for a positive shift.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the exact upper-tail p-value for W+.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Check understanding
Wilcoxon rank-sum tests — objective 4
Maths4U Original · Short practice
Two independent samples have pooled ranks A: \(1,2,3\) and B: \(4,5,6,7\). There are no ties. Test whether A tends to be smaller.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the null expected rank sum for A.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Wilcoxon rank-sum tests — objective 4
Maths4U Original · Short practice
Two independent samples have pooled ranks A: \(2,3,4,5\) and B: \(1,6,7,8,9\). There are no ties. Test whether A tends to be smaller.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the null expected rank sum for A.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.