## Related questions with answers

At Western University the historical mean of scholarship examination scores for freshman applications is 900. Ahistorical population standard deviation $\sigma$= 180 is assumed known. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.

State the hypotheses.

Solutions

VerifiedIn this exercise, we need to find the null $H_0$ hypothesis and the alternative $H_a$ hypothesis. The null hypothesis is the polar opposite of the alternate hypothesis. Researchers work to reject the null hypothesis. Researchers develop the alternative hypothesis that they believe explains a behavior, and then try to disprove the null hypothesis.

The test is concerned with determining whether the mean examination score has changed from the previous score of 900. The alternative hypothesis must then be $\mu\ne900$.

Therefore, the hypotheses for this test are as follows:

$\begin{align*} H_0 &: \mu = 900\\ H_1 &: \mu \neq 900\\ \end{align*}$

In this exercise, we determine the hypotheses corresponding to a hypothesis test about the population mean.

*What are the two types of hypotheses that can be defined?*

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