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
Paired t-tests — objective 1
Maths4U Original · Short practice
For six independent matched pairs, after-minus-before differences are \(11,13,14,16,17,19\). Assume that population differences are normal. Test a positive mean difference.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the mean difference.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Paired t-tests — objective 1
Maths4U Original · Short practice
For six independent matched pairs, after-minus-before differences are \(11,15,17,21,23,27\). Assume that population differences are normal. Test a positive mean difference.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the mean difference.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Method
Paired t-tests — objective 2
Maths4U Original · Short practice
For six independent matched pairs, after-minus-before differences are \(11,15,17,21,23,27\). Assume that population differences are normal. Test a positive mean difference.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the unbiased variance of the differences.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Paired t-tests — objective 2
Maths4U Original · Short practice
For six independent matched pairs, after-minus-before differences are \(11,17,20,26,29,35\). Assume that population differences are normal. Test a positive mean difference.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the unbiased variance of the differences.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Apply
Paired t-tests — objective 3
Maths4U Original · Short practice
For six independent matched pairs, after-minus-before differences are \(11,17,20,26,29,35\). Assume that population differences are normal. Test a positive mean difference.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the t statistic for null mean difference zero.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Paired t-tests — objective 3
Maths4U Original · Short practice
For six independent matched pairs, after-minus-before differences are \(14,16,17,19,20,22\). Assume that population differences are normal. Test a positive mean difference.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the t statistic for null mean difference zero.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Check understanding
Paired t-tests — objective 4
Maths4U Original · Short practice
For six independent matched pairs, after-minus-before differences are \(14,16,17,19,20,22\). Assume that population differences are normal. Test a positive mean difference.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the 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
Paired t-tests — objective 4
Maths4U Original · Short practice
For six independent matched pairs, after-minus-before differences are \(14,18,20,24,26,30\). Assume that population differences are normal. Test a positive mean difference.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the 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.