Normal tests of a population mean · Short practice
Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.
Recall
Normal hypothesis tests and errors — objective 1
Maths4U Original · Short practice
Observations are independent and normal with known \(\displaystyle \sigma =4\). For \(\displaystyle n=25\), test \(H_0:\mu=61\) against \(H_1:\mu>61\). The sample mean is \(62.92\).
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the observed z 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
Normal hypothesis tests and errors — objective 1
Maths4U Original · Short practice
Observations are independent and normal with known \(\displaystyle \sigma =5\). For \(\displaystyle n=25\), test \(H_0:\mu=62\) against \(H_1:\mu>62\). The sample mean is \(64.6\).
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the observed z statistic.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Method
Normal hypothesis tests and errors — objective 2
Maths4U Original · Short practice
Observations are independent and normal with known \(\displaystyle \sigma =5\). For \(\displaystyle n=25\), test \(H_0:\mu=62\) against \(H_1:\mu>62\). The sample mean is \(64.6\).
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the right-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
Normal hypothesis tests and errors — objective 2
Maths4U Original · Short practice
Observations are independent and normal with known \(\displaystyle \sigma =6\). For \(\displaystyle n=25\), test \(H_0:\mu=63\) against \(H_1:\mu>63\). The sample mean is \(66.36\).
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the right-sided p-value.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Apply
Normal hypothesis tests and errors — objective 3
Maths4U Original · Short practice
Observations are independent and normal with known \(\displaystyle \sigma =6\). For \(\displaystyle n=25\), test \(H_0:\mu=63\) against \(H_1:\mu>63\). The sample mean is \(66.36\).
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the sample-mean critical boundary at 5% significance.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Normal hypothesis tests and errors — objective 3
Maths4U Original · Short practice
Observations are independent and normal with known \(\displaystyle \sigma =7\). For \(\displaystyle n=25\), test \(H_0:\mu=64\) against \(H_1:\mu>64\). The sample mean is \(66.24\).
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the sample-mean critical boundary at 5% significance.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Check understanding
Normal hypothesis tests and errors — objective 4
Maths4U Original · Short practice
Observations are independent and normal with known \(\displaystyle \sigma =7\). For \(\displaystyle n=25\), test \(H_0:\mu=64\) against \(H_1:\mu>64\). The sample mean is \(66.24\).
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the two-sided p-value for the same observed z.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Normal hypothesis tests and errors — objective 4
Maths4U Original · Short practice
Observations are independent and normal with known \(\displaystyle \sigma =3\). For \(\displaystyle n=25\), test \(H_0:\mu=65\) against \(H_1:\mu>65\). The sample mean is \(66.08\).
Use a 5% significance level for a written conclusion. A distribution calculator may be used for numerical p-values.
Find the two-sided p-value for the same observed z.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.