12. A pharmaceutical company claims that side effects will be experienced by fewer than 20% of the patients who use medication X. A clinical trial with a random sample of 400 patients was conducted in which half of the patients were randomly assigned to take medication X and the other half received a placebo. Of those that received medication X they find 68 who experienced side effects.

Assuming all conditions for inference were met, which of the following is a 90 percent confidence interval for the proportion of patients that will experience side effects while taking medication X?

(A) (0.1391, 0.2009)
(B) (0.2744, 0.4057)
(C) (0.2849, 0.3951)
(D) (0.6257, 0.7343)
(E) (0.6416, 0.7184)

Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, summarise the data.

A pharmaceutical company claims that side effects will be experienced by fewer than 20% of the patients who use medication X.

A clinical trial with a random sample of 400 patients was conducted in which half of the patients were randomly assigned to take medication X and the other half received a placebo.

Of those that received medication X, they find 68 who experienced side effects.

90% confidence interval for the proportion of patients.

[tex]\rm \hat{p} = \dfrac{68}{200}\\\\\hat{p} = 0.34[/tex]

n = 200

We know that the formula

[tex]\rm \hat{p} \pm z \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

The value of z for a 90% confidence interval is 1.645.

For the positive signs, we have

[tex]0.34+ 1.645 \sqrt{\dfrac{0.34(1-0.34)}{200}}\\\\0.34 + 1.645 *0.03349\\\\0.3951[/tex]

For the negative sign, we have

[tex]0.34- 1.645 \sqrt{\dfrac{0.34(1-0.34)}{200}}\\\\0.34 - 1.645 *0.03349\\\\0.2849[/tex]

Then the interval will be (0.2849, 0.3951)

More about the statistic link is given below.

https://brainly.com/question/10951564