t-distribution: check 1
Difficulty: ★★☆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.
t-distribution: review variant 1
Difficulty: ★★☆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.
t-distribution: check 2
Difficulty: ★★☆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.
t-distribution: review variant 2
Difficulty: ★★☆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.
t-distribution: check 3
Difficulty: ★★☆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.
t-distribution: review variant 3
Difficulty: ★★☆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.
t-distribution: check 4
Difficulty: ★★☆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.
t-distribution: review variant 4
Difficulty: ★★☆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.