Final answer:
To conduct the hypothesis test, define the null and alternative hypotheses, determine the type of test, select an appropriate statistical test, calculate the test statistic, compare it with the critical value or p-value, and then decide whether to reject the null hypothesis based on the result.
Step-by-step explanation:
To conduct a hypothesis test to compare the mean performance score of applicants with a pre-test to those with no pre-test, using a significance level of α = 0.05, first define the null and alternative hypotheses. The null hypothesis (H0) is that the mean score of both groups is the same, while the alternative hypothesis (Ha) would state there is a difference.
Next, decide whether to use a two-tailed or one-tailed test based on the hypothesis. In this scenario, the test appears to be two-tailed as we are looking for equality. Determine the appropriate statistical test (such as a t-test or z-test), based on whether the population standard deviations are known and if the sample size is large enough for the normal approximation to be valid. Gather sample data, calculate the test statistic, and then compare it to the critical value or use the p-value approach to determine if you should reject or fail to reject the null hypothesis.
Ultimately, if the p-value is less than or equal to 0.05, you would reject the null hypothesis, suggesting a significant difference exists. Conversely, if the p-value is greater than 0.05, you do not have enough evidence to reject the null hypothesis and conclude there may be no significant difference.