Question

Consider a drug that is used to help prevent blood clots in certain patients. In clinical​ trials, among 5783 patients treated with this​ drug, 153 developed the adverse reaction of nausea. Use a 0.05 significance level to test the claim that 3​% of users develop nausea. Does nausea appear to be a problematic adverse​ reaction?

Answer 1

Answer:

Based on statistical analysis the claim is of 3% of patients developing adverse reaction is valid and there is a drug problem

Step-by-step explanation:

Here we have

Percentage of patients that develop nausea em= 153/5783 *100 = 2.65 %

To test the hypothesis, we put our null hypothesis as

H₀: μ = 3%

Alternative hypothesis is then

Hₐ: μ < 3%

Therefore the test statistic is

$t=\frac{\hat{p}-p_0}{\sqrt{\frac{ p_0( 1- p_0)}{n}}}$

P₀ = 0.03

$\hat p$ = 0.0265

n = 5783

From the above we have our test statistic as -1.579 from which gives our p value as P = 0.057.

Therefore, as we have our P value less than the confidence level of 0.05, we therefore fail to reject the null hypothesis because there is sufficient statistical evidence that suggest that the proportion of patients who would have adverse reaction to the drug  = 3%.