5.1.2 Hypothesis Tests (Mean and Sigma) - tests concerning the mean and standard deviation of a normal distribution


This statlet tests hypotheses about the mean and standard deviation of a normal distribution. The tabs are:

Input

t test

Power curve

Chi-squared test

Power curve


Input

To use this statlet, enter the following information about your data:

Data label - a name to be displayed on the output.

Sample size - the number of observations in the sample.

Sample mean - the mean of the sample.

Sample standard deviation - the standard deviation of the sample.

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t test

This tab shows the result of a hypothesis test concerning the population mean:

It shows:

Summary statistics.

A confidence interval for the mean.

The result of a t-test run to test a hypothesis about the population mean.

Use the Options button to specify the hypotheses to be tested. If the P-value is less than the alpha risk which you specify, you should reject the null hypothesis at the corresponding significance level.

Options button

Enter:

Null hypothesis - the value of the mean specified by the null hypothesis.

Alt. Hypothesis - select a two-sided test (~=) or a one-sided test.

Alpha - the probability of a Type I error, which is a situation where a true null hypothesis is incorrectly rejected. Typical values for alpha are 10%, 5%, and 1%. The confidence interval is also affected by this setting and uses a confidence level equal to (100-alpha)%.

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Power curve

This tab shows the power curve for the t test:

The power curve shows the probability of rejecting the null hypothesis as a function of the true population mean.

Options button

Same as previous tab.

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Chi-squared test

This tab shows the result of a hypothesis test concerning the population standard deviation

It shows:

Summary statistics.

A confidence interval for the standard deviation.

The result of a chi-squared test run to test a hypothesis about the population sigma.

Use the Options button to specify the hypotheses to be tested. If the P-value is less than the alpha risk which you specify, you should reject the null hypothesis at the corresponding significance level.

Options button

Enter:

Null hypothesis - the value of the standard deviation specified by the null hypothesis.

Alt. Hypothesis - select a two-sided test (~=) or a one-sided test.

Alpha - the probability of a Type I error, which is a situation where a true null hypothesis is incorrectly rejected. Typical values for alpha are 10%, 5%, and 1%. The confidence interval is also affected by this setting and uses a confidence level equal to (100-alpha)%.

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Power curve

This tab shows the power curve for the chi-squared test:

The power curve shows the probability of rejecting the null hypothesis as a function of the true population sigma.

Options button

Same as previous tab.

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