Exercise 19 Refer to the information in the given exercise...

Exercise 19
Refer to the information in the given exercise and do the following.
a. Find the critical value(s).
b. Using a significance level of $\alpha=0.05$, should we reject $H_{0}$ or should we fail to reject $H_{0}$ ?

Key Concepts

Decision Rule

The decision rule specifies whether to reject or fail to reject the null hypothesis based on the comparison between the test statistic and the critical value(s). If the test statistic falls within the rejection region defined by the critical value(s), this provides evidence against the null hypothesis; otherwise, the null hypothesis is not rejected.

Critical Values

Critical values are the threshold points in the distribution of the test statistic that define the boundary of the rejection region. They are determined based on the chosen significance level and the type of test conducted (one-tailed or two-tailed). If the calculated test statistic falls into this rejection region, the null hypothesis is rejected.

Null Hypothesis and Alternative Hypothesis

The null hypothesis (H0) is a statement of no effect or no difference, assumed true until evidence suggests otherwise. The alternative hypothesis (Ha) represents the claim being tested, indicating the presence of an effect or difference. The decision to reject or fail to reject the null is based on how consistent the observed data is with the null hypothesis.

Hypothesis Testing

Hypothesis testing is a statistical procedure that uses sample data to evaluate a hypothesis about a population parameter. This method helps determine whether there is enough evidence to reject a null hypothesis in favor of an alternative hypothesis based on probability thresholds.

Significance Level

The significance level, denoted by ?, represents the threshold probability for rejecting the null hypothesis. It is the maximum allowable probability of making a Type I error (rejecting a true null hypothesis). A common significance level is 0.05, which balances the risk of such an error with the need to detect a true effect.

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