Makers of a new pain-relieving medication claim that it relieves chronic pain faster than the current top-selling pain reliever on the market. A double-blind experiment was conducted in which 10 people who experience chronic pain were randomly selected to take either the new or the current medication. Each of the 10 people recorded the time, in minutes, from taking the medication until pain relief. After an appropriate time period, each of the 10 people took the
other medication and recorded the time from taking the medication until pain relief. The medication each person took
first was randomly determined, and because both medications look the same, the people in the study did not know
which medication was taken first. The table below shows summary statistics for the results.
New Med Old Med Diff
Mean 15.600 16.025 -.425
Stand. 4.811 4.833 1.395
Deviation
Which of the following values is closest to the p-value of the appropriate t-test?
(A) 0.1802
(B) 0.3604
(C) 0.4230
(D) 0.5770
(E) 0.8198
(A) 0.1802
To determine the p-value of the appropriate t-test, we need to compare the mean difference between the two medications to the sampling distribution under the null hypothesis. The null hypothesis states that there is no difference in pain relief time between the new medication and the old medication.
The table provides the mean difference as -0.425, the standard deviation of the differences as 1.395, and the sample size as 10.
To calculate the t-statistic, we use the formula:
t = (mean difference - hypothesized difference) / (standard deviation / √sample size)
In this case, the hypothesized difference is 0 (as stated in the null hypothesis).
t = (-0.425 - 0) / (1.395 / √10)
t = -0.425 / (1.395 / √10)
t ≈ -0.425 / 0.441
t ≈ -0.963
To find the p-value associated with this t-statistic, we can refer to a t-distribution table or use statistical software. The p-value is the probability of obtaining a t-statistic as extreme as the observed one (or more extreme) assuming the null hypothesis is true.
Looking at the provided options, the closest value to the p-value of the appropriate t-test is (A) 0.1802.