Confidence intervals for the difference in means · Short practice
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Recall
Two-sample pooled t inference — objective 1
Maths4U Original · Short practice
Two independent normal populations have a common unknown variance. Sample sizes are 9 and 8, their unbiased variances are 6 and 6, and \(\displaystyle \bar x_1-\bar x_2=\frac{3}{2}\).
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.
Fresh review variant
Two-sample pooled t inference — objective 1
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.
Method
Two-sample pooled t inference — objective 2
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 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.
Fresh review variant
Two-sample pooled t inference — objective 2
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.
Apply
Comparing means with known variances — objective 3
Maths4U Original · Short practice
Independent normal samples have sizes 20 and 22, known population variances 15 and 17, and observed \(\bar x-\bar y=2\). 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.
Fresh review variant
Comparing means with known variances — objective 3
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.
Check understanding
Comparing means with known variances — objective 4
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 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.
Fresh review variant
Comparing means with known variances — objective 4
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.