Question

The value of a test statistic is best described as the basis for deciding whether to: _________

a. reject the null hypothesis.
b. accept the null hypothesis.
c. reject the alternative hypothesis.

Answer 1

The test statistic value informs whether to reject the null hypothesis based on comparing it with a significance level. A hypothesis test evaluates this using data. Reject the null hypothesis if the p-value is less than the alpha level, generally set at 0.05.

Step-by-step explanation:

The value of a test statistic is best described as the basis for deciding whether to reject the null hypothesis. When conducting a hypothesis test, the test statistic helps determine whether the observed data are significantly different from what we would expect under the null hypothesis.

• Null Hypothesis (H0): A statement that there is no effect or no difference, and it is the hypothesis that the test seeks to nullify.
• Alternative Hypothesis (H1 or HA): A statement that indicates the presence of an effect or a difference; it is what you would believe if you reject H0.
• The random variable P' represents a sample proportion in the context of a test of proportion.
• To calculate the test statistic, you would use the observed sample data along with the null hypothesis to compute a value that reflects how much the data deviate from what is expected under H0.
• The p-value is the probability of observing a test statistic at least as extreme as the one calculated, assuming that the null hypothesis is true.
• If the p-value is less than a predetermined significance level (α, typically 0.05), we would typically reject the null hypothesis.
• A Type I error occurs if you incorrectly reject H0 when it is true.
• A Type II error occurs if you incorrectly fail to reject H0 when it is false.
• A decision about the hypothesis is made by comparing the p-value to the significance level (α). A conclusion is then drawn whether to reject or not reject the null hypothesis based on this comparison.
• When testing hypotheses, it's important to note that we never say a hypothesis is proven true or false; rather, we say whether there is or is not enough evidence to reject H0.

If analysis yields a p-value less than α = 0.05, we would reject the null hypothesis.