__Two sample t- test__

To compare means of two samples we need
to apply two-sample t test. **Minitab** **2-Sample-t-test**
function can give us the confidence interval of the difference
between two population means, and perform a hypothesis test.

In exercise 7.36(BPS chapter 7 Page 402) matches the two-sample settings. The Survey of Study Habits and Attitudes(SSHA) was given to male and female first-year students in a selected private school. The data can be entered in two ways. Either both samples are entered in a single column with another column of subscripts to identify the population group (as shown left). Or they can be in separated columns (as shown right). We ues the former as an example here.

Most of the studies suggest that the
mean SSHA score for men is lower than the that in a comparable
group of women. Is this true for first-year students at this college?
To address this question, we can carry out two-sample t test.
Select **Stat->Basic Statistics->2-Sample-t** from the
menu, fill out the dialog box as shown below.

Since we use the sample data
in one column, we checked "**Samples in one column**"
in dialog box and enter the appropriate column names under "**Sample**:"
and "**Subscripts**:". Since the hypothesis are:

we select the greater than alternative.

The outcome
shows the **P-value **was 0.024, so we have convincing evidence
to reject the null hypothesis that the mean score for female and
male first-year students in this school is the same. The output
also show us the 95% C.I. for
is (0.3, 39.4).

The **Graphs...**
button could produce a graph illustrating the differences between
the two groups. We must take a look of the graph, before we check
the box of " Assuming equal variances". It would give
us evidence whether the variances are close or not. In this example,
we didn't assume two populations have same variance.

Unless we check " **Assuming equal
variances**" box, **Minitab** would not assume that
the population have equal variances, so the test statistic is
, with degree of freedom . If we did check " **Assuming
equal variances**" box, Minitab would use pooled sample
variance with *df*=n1+n2-2 to calculate test
statistic.