Final answer:
The student's question pertains to statistical hypothesis testing, involving concepts like sensitivity, Type I and II errors, the empirical rule, and the use of alpha levels and p-values to determine statistical significance.
Step-by-step explanation:
The student's question seems to concern the evaluation of a statistical hypothesis testing scenario, particularly involving the use of p-value, alpha level, and possibly errors in hypothesis testing. When a sensitivity of .95 is mentioned, it typically refers to the test's ability to correctly identify true positives. Meanwhile, a negative test result means that the test indicates the absence of a condition or feature tested for.
The rules about ruling in or ruling out these options would likely refer to whether we can confidently determine the presence or absence of a feature or condition based on the test result and given the test's sensitivity or specificity.
Checking a student's solution that involves an alpha of 0.05 and a decision to reject the null hypothesis based on a p-value less than alpha is a standard approach in hypothesis testing. This assumes that there is sufficient evidence against the null hypothesis at the 5 percent level of significance.
Type I and Type II errors are critical concepts in hypothesis testing. A Type I error occurs when we incorrectly reject a true null hypothesis, while a Type II error occurs when we fail to reject a false null hypothesis.
The empirical rule mentioned, also known as the 68-95-99.7 rule, relates to the percentage of values within certain numbers of standard deviations from the mean in a normal distribution -- approximately 68% within one standard deviation, 95% within two, and 99.7% within three.
Finally, to check if the data fit a particular distribution or to evaluate hypotheses about population parameters, statistical tests such as the chi-square test or z-tests might be used. These will typically rely on critical values and rejection regions defined by the alpha level.