Question

Two types of medication for hives are being tested to determine if there is a difference in the proportions of adult patient reactions. Twenty out of a random sample of 200 adults given medication A still had hives 30 minutes after taking the medication. Twelve out of another random sample of 180 adults given medication B still had hives 30 minutes after taking the medication. Test at a 1% level of significance.

1. (Write all answers as a decimal rounded to the 3rd decimal place)

  Determine the point estimator of Medicine A:

Determine the point estimator of Medicine B:

Determine your test statistic:

Determine your p-value:

  Determine significance level:

2. What would be your formal conclusion?

A. Accept the null hypothesis B. Reject the null hypothesis C. Fail to reject the null hypothesis  D. Fail to accept the null hypothesis

3. What practical conclusion can we make about the claim? (Answer as a complete sentence)

4. Determine the point estimator of Medication A as a reduced fraction:

  Determine the point estimator of Medication B as a reduced fraction:

5. Now we are going to keep the point estimator the same but change the sample size.

What would be your p-value if the sample size for both sets doubled (Sample for Medicine A was out of 400 people, Sample for Medicine B was out of 360 people)? (Round to the 3rd decimal place)

What would be your p-value if the sample size for both sets tripled (Sample for Medicine A was out of 600 people, Sample for Medicine B was out of 540 people)? (Round to the 3rd decimal place)

What would be your p-value if the sample size for both sets quadrupled (Sample for Medicine A was out of 800 people, Sample for Medicine B was out of 720 people)? (Round to the 3rd decimal place)

Answer 1

Solution:

Here, we have to use two sample z-test for population proportions.

H₀: p₁ = p₂ versus H_a: p₁ ≠ p₂

(Two tailed test)

We are given

X1 = 20, N1 = 200

X2=12, N2 = 180

Determine the point estimator of Medicine A:

Point estimator of Medicine A = P1 = X1/N1 = 20/200 = 0.100

Determine the point estimator of Medicine B:

Point estimator of Medicine B = P2 = X2/N2 = 12/180 = 0.067

Determine your test statistic:

Average proportion = (X1+X2)/(N1+N2) = (20+12)/(200+180) = 0.084211

Test statistic formula is given as below:

Z = (P1 – P2) / sqrt(P*(1 – P)*((1/N1) + (1/N2)))

Z = (0.100 - 0.067) / sqrt(0.084211*(1 – 0.084211)*((1/200) + (1/180)))

Z = 0.033/ sqrt(0.084211*(1 – 0.084211)*((1/200) + (1/180)))

Z = 1.1683

Determine your p-value:

P-value = 0.2427

(by using z-table)

Determine significance level:

α = 0.01

2. What would be your formal conclusion?

P-value > α = 0.01

So, we do not reject the null hypothesis

C. Fail to reject the null hypothesis

3. What practical conclusion can we make about the claim?

There is insufficient evidence to conclude that there is a difference in the proportions of adult patients reactions.

4. Determine the point estimator of Medication A as a reduced fraction: P1 = 0.100

  Determine the point estimator of Medication B as a reduced fraction: P2 = 0.067