Chapter 11.1, Problem 7E

A test was made of $H_0:{\mu }_1={\mu }_2$ versus $H_1:{\mu }_1<{\mu }_2.$

The sample means were ${\bar{x}}_1=6$ and ${\bar{x}}_2=11$, the sample standard deviations were $s_1=3$ and $s_2=5$, and the sample sizes were $n_1=10$ and $n_2=20.$

1. How many degrees of freedom are there for the test statistic, using the simple method?
2. Compute the value of the test statistic.
3. Is $H_0$ rejected at the 0.05 level? Explain.