# 9.2.2.1 - Minitab Express: Independent Means t Test

9.2.2.1 - Minitab Express: Independent Means t Test

Here we will use Minitab Express to conduct an independent means t test. Note that Minitab Express uses a more complicated formula for computing the degrees of freedom for this test. To read more about the formulas that Minitab Express uses, see Minitab Express Support.

Within Minitab Express, the procedure for obtaining the test statistic and confidence interval for independent means is identical.

## MinitabExpress – Conducting an Independent Means t Test

Let's compare the mean SAT-Math scores of students who have and have not ever cheated. Both sample sizes are at least 30 so the sampling distribution can be approximated using the $t$ distribution.

1. Open the Minitab Express file:
2. On a PC: In the menu bar select STATISTICS > Two Samples > t
3. On a Mac: In the menu bar select Statistics > 2-Sample Inference > t
4. Double click the variable SATM in the box on the left to insert the variable into the Samples box
5. Double click the variable Ever Cheat in the box on the left to insert the variable into the Sample IDs box
6. Click OK

This should result in the following output:

2-Sample t: SATM by Ever Cheat
 $\mu_1$: mean of SATM when Ever Cheat = No $\mu_2$: mean of SATM when Ever Cheat = Yes Difference: $\mu_1-\mu_2$

Equal variances are not assumed for this analysis.

Descriptive Statistics: SATM
Ever Cheat N Mean StDev SE Mean
No 163 603.988 86.893 6.806
Yes 53 583.68 79.18 10.88
Estimation for Difference
Difference 95% CI for Difference
20.31 (-5.16, 45.78)
Null hypothesis $H_0$: $\mu_1-\mu_2=0$ $H_1$: $\mu_1-\mu_2\neq0$
T-Value DF P-Value
1.58 95 0.1168
Video Walkthrough

Select your operating system below to see a step-by-step guide for this example.

The result of our two independent means t test is $t(95) = 1.58, p = 0.1168$. Our p-value is greater than the standard alpha level of 0.05 so we fail to reject the null hypothesis. There is not evidence to state that the mean SAT-Math scores of students who have and have not ever cheated are different.

Note that we could also interpret the confidence interval in this output. We are 95% confident that the mean difference in the population is between -5.16 and 45.78.

The example above uses a dataset. The following examples show how you can conduct this type of test using summarized data.

# 9.2.2.1.1 - Video Example: Weight by Treatment, Summarized Data

9.2.2.1.1 - Video Example: Weight by Treatment, Summarized Data

Research question: Do patients who receive our treatment weigh less than participants who do not receive our treatment?

Participants were randomly assigned to the treatment condition or a control group. After our intervention, their weights were measured in pounds. Weight is a quantitative variable, so we are going to be comparing means in this example. If assumptions are met, we’ll be conducting a two independent means t test.

Our treatment group has a sample size of 45, mean of 140 pounds, and standard deviation of 20 pounds. Our control group has a sample size of 40, sample mean of 150 pounds, and standard deviation of 25 pounds.

The video below walks through the five-step hypothesis testing procedure to analyze these data in Minitab Express.

# 9.2.2.1.3 - Example: Height by Sex

9.2.2.1.3 - Example: Height by Sex

This example uses the following dataset:

CLASS_SURVEY.MTW

Research Question: In the population of all college students, is the mean height of females less than the mean height of males?

Data concerning height (in inches) were collected from 99 females and 126 males.

1. Check assumptions and write hypotheses

We have two independent groups: females and males. Height in inches is a quantitative variable. This means that we will be comparing the means of two independent groups.

There are 126 females and 99 males in our sample. The sampling distribution will be approximately normally distributed because both sample sizes are at least 30.

This is a left-tailed test because we want to know if the mean for females is less than the mean for males.

(Note: Minitab Express will arrange the levels of the explanatory variable in alphabetical order. This is why "females" are listed before "males" in this example.)

$H_{0}:\mu_f = \mu_m$
$H_{a}: \mu_f < \mu_m$

2. Calculate the test statistic
1. Open the Minitab Express file:
2. On a PC: In the menu bar select STATISTICS > Two Samples > t
On a Mac: In the menu bar select Statistics > 2-Sample Inference > t
3. Double click the variable Height in the box on the left to insert the variable into the Samples box
4. Double click the variable Gender in the box on the left to insert the variable into the Sample IDs box
5. Click OK

This should result in the following output:

2-Sample t: Height by Gender
 $\mu_1$: mean of Height when Gender = Female $\mu_2$: mean of Height when Gender = Male Difference: $\mu_1-\mu_2$

Equal variances are not assumed for this analysis.

Descriptive Statistics: Height
Gender N Mean StDev SE Mean
Female 126 65.6190 6.5322 0.5819
Male 99 70.2424 3.6340 0.3652
Estimation for Difference
Difference 95% Upper Bound for Difference
-4.6234 -3.4881
Null hypothesis $H_0$: $\mu_1-\mu_2=0$ $H_1$: $\mu_1-\mu_2<0$

T-Value DF P-Value
-6.73 202 <0.0001

The test statistic is t = -6.73

3. Determine the p-value

From the output given in Step 2, the p value is <0.0001

4. Make a decision

$p\leq.05$, therefore we reject the null hypothesis.

5. State a "real world" conclusion

There is evidence that the mean height of female students is less than the mean height of male students in the population.

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