Question

Consider a drug that is used to help prevent blood clots in certain patients. In clinical trials, among 5764 patients treated with this drug, 152 developed the adverse reaction of nausea. Use a 0.10 significance level to test the claim that 3% of users develop nausea. Does nausea appear to be a problematic adverse reaction? Identify the null and alternative hypotheses for this test. Choose the correct answer below. O A. Ho:p=0.03 Hy: p = 0.03 B. Ho: p = 0.03 H1: p<0.03 0 C. Ho: p = 0.03 H :p>0.03 Ô D. Ho: p = 0.03 Hy:p0.03 Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is (Round to two decimal places as needed.)

Answer 1

Solution:

Here, we have to use one sample z test for the population proportion.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: The percentage of patients who developed the adverse reaction of nausea is 3%.

Alternative hypothesis: H₁: The percentage of patients who developed the adverse reaction of nausea is different than 3%.

H₀: p = 0.03

H₁: p ≠ 0.03

(Answer: D)

This is a two tailed test.

We are given

Level of significance = α = 0.10

Test statistic formula for this test is given as below:

Z = (p̂ - p)/sqrt(pq/n)

Where, p̂ = Sample proportion, p is population proportion, q = 1 - p, and n is sample size

x = number of items of interest = 152

n = sample size = 5764

p̂ = x/n = 152/ 5764 = 0.026370576

p = 0.03

q = 1 - p = 0.97

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.026370576 - 0.03)/sqrt(0.03*0.97/5764)

Z = -1.6153

The test statistic for this hypothesis test is -1.62.

P-value = 0.105

(by using z-table)

The P-value for this hypothesis test is 0.105.

P-value > α = 0.10

So, we do not reject the null hypothesis

B. Fail to reject H₀. There is not sufficient evidence to warrant rejection of the claim that 3% of users develop nausea.

Since the rate of nauseas appears to be relatively low, it is not a problematic adverse reaction.