What do we call the conditions under which the null hypothesis is not rejected?
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A. B. C. D. E.B
The decision rule lays out the conditions under which we may compare the z values and decide whether or not to reject the hypothesis.
In the context of hypothesis testing, the conditions under which the null hypothesis is not rejected are referred to as the "decision rule."
Hypothesis testing is a statistical method used to make inferences or draw conclusions about a population based on a sample of data. It involves formulating a null hypothesis (H₀) and an alternative hypothesis (H₁). The null hypothesis represents the status quo or the default position, while the alternative hypothesis proposes a deviation from the null hypothesis.
The decision rule is a set of criteria or conditions that determine whether to reject the null hypothesis or fail to reject it based on the sample data. It is typically based on a test statistic and a predetermined significance level (α).
The test statistic is a numerical value calculated from the sample data and is used to quantify the extent to which the sample supports or contradicts the null hypothesis. It measures the difference between the observed data and what is expected under the null hypothesis. The test statistic can vary depending on the hypothesis test being performed (e.g., t-statistic, z-statistic, F-statistic, etc.).
To make a decision about the null hypothesis, the test statistic is compared to a critical value. The critical value is a threshold value determined by the chosen significance level (α) and the distribution of the test statistic under the null hypothesis. If the test statistic falls in the critical region (the region where extreme values of the test statistic would lead to rejection of the null hypothesis), the null hypothesis is rejected. If the test statistic falls outside the critical region, the null hypothesis is not rejected.
Therefore, in the given question, the correct answer is B. Decision rule, as it refers to the conditions under which the null hypothesis is not rejected. The other options are not applicable to this particular aspect of hypothesis testing:
A. Critical value: Critical value is the threshold value used to define the critical region and determine whether to reject the null hypothesis. It is involved in the decision rule.
C. Alternate hypothesis: The alternative hypothesis proposes a deviation from the null hypothesis. It is an alternative explanation or claim to be tested against the null hypothesis.
D. None of these answers: This option is incorrect because the correct answer is B.
E. Test statistic: The test statistic quantifies the difference between the observed data and what is expected under the null hypothesis. It is used in the decision rule to determine whether to reject the null hypothesis. However, it is not specifically called the conditions under which the null hypothesis is not rejected.