Maths4U Original · Short practice

Two independent normal populations have a common unknown variance. Sample sizes are 10 and 9, their unbiased variances are 7 and 7, and \(\bar x_1-\bar x_2=2\).

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

Find the pooled variance estimate.

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 7 and 10, their unbiased variances are 4 and 5, and \(\displaystyle \bar x_1-\bar x_2=\frac{5}{2}\).

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

Find the pooled variance estimate.

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 7 and 10, their unbiased variances are 4 and 5, and \(\displaystyle \bar x_1-\bar x_2=\frac{5}{2}\).

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

Find the standard error of the mean difference.

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 standard error of the mean difference.

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

Independent normal samples have sizes 21 and 23, known population variances 16 and 18, and observed \(\displaystyle \bar x-\bar y=\frac{5}{2}\). Test \(H_0:\mu_X=\mu_Y\) against \(H_1:\mu_X>\mu_Y\).

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

Independent normal samples have sizes 22 and 24, known population variances 17 and 19, and observed \(\bar x-\bar y=3\). Test \(H_0:\mu_X=\mu_Y\) against \(H_1:\mu_X>\mu_Y\).

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

Independent normal samples have sizes 22 and 24, known population variances 17 and 19, and observed \(\bar x-\bar y=3\). Test \(H_0:\mu_X=\mu_Y\) against \(H_1:\mu_X>\mu_Y\).

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% confidence interval for the mean difference.

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

Independent normal samples have sizes 23 and 25, known population variances 18 and 20, and observed \(\bar x-\bar y=1\). Test \(H_0:\mu_X=\mu_Y\) against \(H_1:\mu_X>\mu_Y\).

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% confidence interval for the mean difference.

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