Describe the process for testing a hypothesis about two population means when the samples are independent and small.

Question

Quizplus · Accepted Answer

The Answer is The hypotheses are

\mathrm { H } _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0

and

\mathrm { H } _ { 1 } : \mu _ { 1 } - \mu _ { 2 } eq 0

. The test statistic is

\mathrm { t } = \frac { \overline { ( x 1 } - \bar { x } 2 ) - \left( \mu _ { 1 } - \mu _ { 2 } ight) } { \sqrt { \frac { \mathrm { s } _ { 1 } ^ { 2 } } { \mathrm { n } _ { 1 } } + \frac { \mathrm { s } _ { 2 } ^ { 2 } } { \mathrm { n } _ { 2 } } } }

. The critical value(s) are obtained using the

\mathrm { t } - \mathrm { table }

. The value of the test statistic is compared with the critical value(s) and the null hypothesis is rejected if the test statistic falls in the critical region (which will happen if the difference between the sample means is sufficiently different from zero).
Alternatively, The P-value can be obtained using the

t

-table and the null hypothesis is rejected if the

\mathrm { P }

-value is smaller than the significance level.

Describe the Process for Testing a Hypothesis About Two Population