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.

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

Answer 1

Answer :

given data :-

random sample of adults : n = 200

level of significance : = 0.01

• There are two sorts of prescriptions A and B.
• The producer guarantees that the new drug B is more compelling than the standard prescription An and attempts a correlation with decide whether medicine B produces alleviation for a higher extent of grown-up patients inside a 30-minute time window.

(a) now we need to find out the null and alternative hypotheses in words and in statistical symbols :-

The theory for the test is,

H0: Pa = Pb Vs Pa < Pb

In wording :

• H0 : new drug B is less powerful than the standard medicine A.
• H1 : new drug B is more powerful than the standard medicine A

(b) the test is fitting to utilize is :-

Here we will utilize two extent z-test.

Here example size is 200 which is excessively huge so we will go to tow test z-test.

(c) the test be right-tailed, left-tailed or two-tailed :-

The test is left followed and hence this is one followed test.

(d) the outcome that would result in a Type I error :-

• Type I blunder = P(Reject H0/H0 genuine)

= P(new prescription B is more compelling than the standard drug A/new medicine B is less viable than the standard prescription A.)

• Type I mistake we signify by alpha.

(e) the outcome that would result in a Type II error :-

• Type II blunder = P(Accept H0/H1 is valid)

= P(new medicine B is less compelling than the standard prescription A. /new drug B is more viable than the standard prescription A)

• Type II blunder we signify by beta.