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Recall
One-sample t inference — objective 1
Maths4U Original · Short practice
A random sample of 10 independent normal observations has mean 31 and unbiased sample standard deviation 4. Test \(H_0:\mu=30\) against an increase; the population variance is unknown.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the observed t 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
One-sample t inference — objective 1
Maths4U Original · Short practice
A random sample of 11 independent normal observations has mean 32.5 and unbiased sample standard deviation 5. Test \(H_0:\mu=31\) against an increase; the population variance is unknown.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the observed t statistic.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Method
One-sample t inference — objective 2
Maths4U Original · Short practice
A random sample of 11 independent normal observations has mean 32.5 and unbiased sample standard deviation 5. Test \(H_0:\mu=31\) against an increase; the population variance is unknown.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
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
One-sample t inference — objective 2
Maths4U Original · Short practice
A random sample of 6 independent normal observations has mean 34 and unbiased sample standard deviation 2. Test \(H_0:\mu=32\) against an increase; the population variance is unknown.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
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.
Apply
One-sample t inference — objective 3
Maths4U Original · Short practice
A random sample of 6 independent normal observations has mean 34 and unbiased sample standard deviation 2. Test \(H_0:\mu=32\) against an increase; the population variance is unknown.
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
One-sample t inference — objective 3
Maths4U Original · Short practice
A random sample of 7 independent normal observations has mean 35.5 and unbiased sample standard deviation 3. Test \(H_0:\mu=33\) against an increase; the population variance is unknown.
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.
Check understanding
One-sample t inference — objective 4
Maths4U Original · Short practice
A random sample of 7 independent normal observations has mean 35.5 and unbiased sample standard deviation 3. Test \(H_0:\mu=33\) against an increase; the population variance is unknown.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the half-width of a two-sided 95% t confidence interval.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
One-sample t inference — objective 4
Maths4U Original · Short practice
A random sample of 8 independent normal observations has mean 37 and unbiased sample standard deviation 4. Test \(H_0:\mu=34\) against an increase; the population variance is unknown.
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the half-width of a two-sided 95% t confidence interval.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.