# 5.3.1- Steps in Conducting a Hypothesis Test for $$\mu$$

5.3.1- Steps in Conducting a Hypothesis Test for $$\mu$$
1. Step 1: Set up the hypotheses and check conditions
One Mean t-test Hypotheses

$$H_0\colon \mu=\mu_0$$

$$H_a\colon \mu\ne \mu_0$$

Conditions: The data comes from an approximately normal distribution or the sample size is at least 30

2. Step 2: Decide on the significance level, $$\alpha$$

Typically, 5%. If $$\alpha$$ is not specified, use 5%

3. Step 3: Calculate the test statistic

One Mean t-test: $$t^*=\dfrac{\bar{x}-\mu_0}{\frac{s}{\sqrt{n}}}$$

4. Step 4: Compute the appropriate p-value based on our alternative hypothesis

Typically we will let Minitab handle this for us. But if you are really interested, you can look p values up in probability tables found in the appendix of your textbook!

5. Step 5: Make a decision about the null hypothesis

If the p-value is less than the significance level, $$\alpha$$, then reject $$H_0$$ (and conclude $$H_a$$). If it is greater than the significance level, then do not reject $$H_0$$.

6. Step 6

State an overall conclusion.

## Conduct a One-Sample Mean t-Test

Note that these steps are very similar to those for one-mean confidence interval. The differences occur in steps 4 through 8.

To conduct the one sample mean t-test in Minitab...

1. Choose Stat > Basic Stat > 1 Sample t.
2. In the drop-down box use "One or more samples, each in a column" if you have the raw data, otherwise select "Summarized data" if you only have the sample statistics.
3. If using the raw data, enter the column of interest into the blank variable window below the drop down selection. If using summarized data, enter the sample size, sample mean, and sample standard deviation in their respective fields.
4. Choose the check box for "Perform hypothesis test" and enter the null hypothesis value.
5. Choose Options.
6. Enter the confidence level associated with alpha (e.g. 95% for alpha of 5%).
7. From the drop down list for "Alternative hypothesis" select the correct alternative.
8. Click OK and OK.

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