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.

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 observed t statistic.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

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.

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 degrees of freedom.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

Two independent normal populations have a common unknown variance. Sample sizes are 8 and 11, their unbiased variances are 5 and 6, and \(\bar x_1-\bar x_2=3\).

Use \(\displaystyle H_{1}: \mu _{1}>\mu _{2}\) and a 5% significance level for the written test conclusion.

Find the t statistic for equal population means.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

Two independent normal populations have a common unknown variance. Sample sizes are 9 and 12, their unbiased variances are 6 and 7, and \(\displaystyle \bar x_1-\bar x_2=\frac{7}{2}\).

Use \(\displaystyle H_{1}: \mu _{1}>\mu _{2}\) and a 5% significance level for the written test conclusion.

Find the t statistic for equal population means.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

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 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.

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.