Question

A particular surgical procedure has a long recovery time. A team of researchers carry out atest for a drug known to promote tissue repair could reduce the recovery time. They recruite75 volunteers who agreed to take part in a double blind trial following their surgery. Two thirds of these patients were given the active drug and the remaining third were given thea placebo. The researchers hope to find evidence that the drug is correlated with shorterrecovery times. They are aware that the distribution of recovery times is strongly skewedso they decide to compare the medians of the recovery times rather than the means. The null hypothesis that they hoped they would find evidence against was that:

The median recovery time for patients who take a treatment of the drug after theirsurgery is equal to the median recovery time for patients who take a placebo.The team wrote out several possible statements for the alternative hypotheses. These are:

Option A: On average the patients taking the drug recover in fewer days that those takingthe placebo.

Option B: The median recovery time for patients who take the drug treatment is lowerthan for patients who take the placebo treatment.

Option C: Patients who take a treatement of the drug after their surgery have a differentmedian recovery time than those patients who take a placebo.

Option D: The drug helps patients recover from the surgery.

Option E: The median recovery time for patients who take the drug treatment is higherthan for patients who take the placebo treatment.

For each option give a brief comment on how appriate it would be to use the statementas the alternative.

Answer 1

Let the median recovery time for patients who take a treatment of the drug after their surgery = m1

And Let the median recovery time median recovery time for patients who take a placebo = m2

The null hypothesis, H0: m1 = m2

• Option A - On average the patients taking the drug recover in fewer days that those taking the placebo.

The main variable of focus here is the median time and not the average time. So, the statement in Option A is not appropriate Statement for the Alternate Hypothesis

• Option B - The median recovery time for patients who take the drug treatment is lower than for patients who take the placebo treatment.

The above statement is a valid statement for the Alternate Hypothesis, which states that m1 < m2

Therefore,

The null hypothesis, H0: m1 = m2 and the

Alternate Hypothesis, Ha: m1 < m2

This is one – sided test.

• Option C - Patients who take a treatment of the drug after their surgery have a different median recovery time than those patients who take a placebo

The above statement is a valid statement for the Alternate Hypothesis, which states that m1 ≠ m2

Therefore,

The null hypothesis, H0: m1 = m2 and the

Alternate Hypothesis, Ha: m1 ≠ m2

This is a two – sided test

• Option D - The drug helps patients recover from the surgery.

The above statement is an invalid statement for the alternate hypothesis. It is just a statement regarding the recovery of patients that use the drug for treatment.

• Option E - The median recovery time for patients who take the drug treatment is higher than for patients who take the placebo treatment.

The above statement is a valid statement for the Alternate Hypothesis, which states that m1 > m2

Therefore,

The null hypothesis, H0: m1 = m2 and the

Alternate Hypothesis, Ha: m1 > m2

This is one – sided test.

Therefore, from the above given options, Option B, C & E are the proper statements for the Alternate Hypothesis.