## Related questions with answers

Consider the following hypothesis test:

$\begin{array} { l } { H _ { 0 } : \mu \leq 25 } \\ { H _ { \mathrm { a } } : \mu > 25 } \end{array}$

A sample of 40 provided a sample mean of 26.4. The population standard deviation is 6.

What is the rejection rule using the critical value? What is your conclusion?

Solutions

VerifiedIn this exercise, we need to evaluate the rejection rule using the critical value approach. The critical value is the biggest value of the test statistic that leads to the null hypothesis being rejected. For Upper Tail Test, we reject the null hypothesis $H_0$ if the test statistics $z$ is greater than or equal to the critical value $z_a$.

We can also reject the null hypothesis if the value of test statistic is located inside the critical region.

Given:

- $\overline{x}$ = Sample mean = 26.4
- $\sigma$ = Population standard deviation = 6
- $n$ = Sample size = 40
- $\alpha$ = Significance level = 0.01
- $H_0:\mu\leq 25$, $H_a:\mu>25$

In this exercise, we determine the conclusion of a hypothesis test about a population mean when the population standard deviation $\sigma$ is known.

*How do you execute a hypothesis test?*

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