Question

Test H0: m £ 8 versus HA: m > 8, given a = 0.01, n = 25, =8.13 and s = 0.25. Assume the sample is selected from a normally distributed population.

Answer 1

Answer on Question #54036 - Math - Statistics and Probability

Test $H_0: \mu \leq 8$ versus $H_a: \mu > 8$, given $\alpha = 0.01$, $n = 25$, $\bar{x} = 8.13$ and $s = 0.25$. Assume the sample is selected from a normally distributed population.

Solution

$H_0: \mu \leq 8$ $H_a: \mu > 8$

The test statistic is

$$t = \frac {\bar {x} - 8}{\frac {s}{\sqrt {n}}} = \frac {8.13 - 8}{\frac {0.25}{\sqrt {25}}} = 2.6.$$

The critical value for $\alpha = 0.01$ significance level and $25 - 1 = 24$ degrees of freedom is $t_{cr} = 2.492$.

Because $t = 2.6 > t_{cr} = 2.492$ we reject the null hypothesis. There is a sufficient evidence to conclude that $\mu > 8$.

www.AssignmentExpert.com