## Hypothesis Test for Two Means

- When to use it: To test the difference of two sample means when population variances are unknown but considered equal

For more informations about Hypothesis Test for Two Means click here.

## Example

Let's compare certain engine head dimensions from two different production lines. A sample of 10 items was taken from line 1 and a sample of 12 items was taken from line 2.

The null hypothesis: The means are equal using \( \alpha = 0.05 \)

H_{0}: \( \mu_1 = \mu_2 \) H_{a}: \( \mu_1 \neq \mu_2 \)

We calculate t as: \( t = \displaystyle \frac{\bar{X}_1 - \bar{X}_2}{\displaystyle s_p \sqrt{ \frac{1}{n_1} + \frac{1}{n_2}}} \)

## Using Excel:

First one needs to check if the DATA ANALYSIS menu is activated: Under DATA select DATA ANALYSIS. If it’s empty, then select EXCEL OPTIONS, ADD-INS, GO and select ANALYSIS TOOLPAK and ANALYSIS TOOLPAK- VBA and hit ok. The toolpaks may need to be installed. Go again to the DATA ANALYSIS menu and you should see the following image:

In the Data Analysis toolbox, scroll down and select t-Test: Two-Sample Assuming Equal Variances. Input appropriate column ranges for the data, the hypothesized mean difference, and an alpha value (default = 0.05).

Excel should calculate the following:

We can see that the null hypothesis is not rejected for a two-sided t-test. (p-value = 0.568 > 0.05 = \( \alpha \))

## Running a two sample Z test:

## Do it yourself

Step 1: Go to "Attachments" on the bottom of this page and dowload the Excel spreadsheet.

Step 2: Follow the steps teached in the video above and solve the exercises in the Excel spredsheet dowloaded.

Step 3: Answer the questions in the Interactive Content below.

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