Question

Two types of medication for hives are being tested. The manufacturer claims that the new medication B is more effective than the standard medication A and undertakes a comparison to determine if medication B produces relief for a higher proportion of adult patients within a 30-minute time window. 20 out of a random sample of 200 adults given medication A still had hives 30 minutes after taking the medication. 12 out of another random sample of 200 adults given medication B still had hives 30 minutes after taking the medication. The hypothesis test is to be carried out at a 1% level of significance.

1. State the null and alternative hypotheses in words and in statistical symbols.
2. What statistical test is appropriate to use? Explain the rationale for your answer.
3. Would the test be right-tailed, left-tailed or two-tailed? Explain the rationale for your answer.
4. Describe an outcome that would result in a Type I error. Explain the rationale for your answer.
5. Describe an outcome that would result in a Type II error. Explain the rationale for your answer.

Answer 1

Answer:

a)

Let us assume p1 be the extent of grown-ups given drug A get help 30 minutes in the wake of taking the prescription

p2 be the extent of grown-ups given prescription B get help 30 minutes in the wake of taking the medicine.

Hypothesis are given as follows

Null hypothesis:

It is the extent of grown-ups given prescription A get alleviation 30 minutes in the wake of taking the medicine is more than equivalent to extent of grown-ups given drug B get help 30 minutes in the wake of taking the prescription .

Ho: p1≥ p2

Alternate hypothesis:

It is the extent of grown-ups given drug A get alleviation 30 minutes in the wake of taking the medicine is not exactly the extent of grown-ups given prescription B get help 30 minutes subsequent to taking the medicine.

H1: p1 < p2

b)

Since we have to look at two extent / proportions to compare , so z test ought to be utilized.

c)

Here the test is to be left tailed

d)

Type I mistake is the likelihood of dismissing the genuine null hypothesis.

That is analyst presume that drug B produces help for a higher extent of grown-up patients inside a 30-minute time window while really prescription B doesn't deliver alleviation for a higher extent of grown-up patients inside a 30-minute time window.

e)

Type II mistake is the likelihood of neglect to dismiss the fake null hypothesis.

That is specialist presume that drug B doesn't create alleviation for a higher extent of grown-up patients inside a 30-minute time window while really prescription B produces help for a higher extent of grown-up patients inside a 30-minute time window.