Paired tests and test selection：練習問題

A psychologist uses a Wilcoxon signed-rank test to compare reaction times of 10 participants before and after drinking coffee. One participant had the exact same reaction time in both trials.

According to standard procedure for the Wilcoxon signed-rank test in the Edexcel specification, how should this 'zero difference' be handled?

A researcher is comparing the effectiveness of two different fertilizers, A and B, on the yield of tomato plants. 10 plots of land are divided into pairs based on soil quality (Blocking). One plot in each pair receives Fertilizer A and the other Fertilizer B.

The yields (in kg) are recorded. To use a paired t-test to determine if Fertilizer A produces a higher yield, which of the following assumptions must be met?

A clinical trial compares a new blood pressure medication to a placebo using a paired design with 15 patients. The differences in systolic blood pressure (Placebo - Medication) are recorded. A sign test is performed to determine if the medication reduces blood pressure. Out of the 15 patients, 12 showed a decrease in blood pressure, 2 showed an increase, and 1 showed no change.

Using a 5% significance level for a one-tailed test, what is the conclusion? (Given that for \(n = 14\), \(P(X \ge 12) = 0.0065\) and \(P(X \ge 10) = 0.0898\) where \(X \sim B(14, 0.5)\)).

A researcher is conducting a study to compare the effectiveness of two different sleep aids on the same group of 12 volunteers. The difference in hours of sleep (Treatment A - Treatment B) for each volunteer is calculated. The researcher intends to perform a Wilcoxon signed-rank test to see if there is a significant difference in the median sleep time.

Which of the following is a necessary assumption for the Wilcoxon signed-rank test to be valid in this paired context?

A researcher conducts a one-tailed sign test on 20 pairs of data to see if a treatment has a positive effect. There are 15 positive differences, 3 negative differences, and 2 zeros.

Using a 5% significance level, what is the critical value for the test statistic \(X\) (number of negative differences), and what is the conclusion?
(Table values for \(B(18, 0.5)\): \(P(X \le 4) = 0.0154\), \(P(X \le 5) = 0.0481\), \(P(X \le 6) = 0.1189\))

When conducting a paired t-test to compare the reaction times of 12 participants before and after a stimulus, what specific assumption must be made about the distribution of the differences for the test to be valid?