Solve the Problem $\mathrm { p }$ Can Be Written As $\mathrm { p } < \hat { \mathrm { p } } + \mathrm { E }$

question 19

Multiple Choice

Solve the problem.
-A one-sided confidence interval for $\mathrm { p }$ can be written as $\mathrm { p } < \hat { \mathrm { p } } + \mathrm { E }$ or $\mathrm { p } > \hat { \mathrm { p } } - \mathrm { E }$ where the margin of error $\mathrm { E }$ is modified by replacing $\mathrm { z } _ { \alpha / 2 }$ with $\mathrm { z } _ { \alpha }$ . If a teacher wants to report that the fail rate on a test is at most $x$ with $90 \%$ confidence, construct the appropriate one-sided confidence interval. Assume that a simple random sample of 74 students results in 8 who fail the test.

• A) \(\mathrm { p } < 0.167\)
• B) \(\mathrm { p } < 0.154\)
• C) \(\mathrm { p } < 0.062\)
• D) \(p > 0.062\)

---

Definitions:

Infection

The invasion and multiplication of microorganisms such as bacteria, viruses, and parasites that are not normally present within the body.

Chronic

Referring to a health condition or disease that is persistent or otherwise long-lasting in its effects, often for the lifetime of the person affected.

Hepatitis

Inflammation of the liver, often caused by viral infections, alcohol abuse, or other health conditions.

Pathogens

Microorganisms such as bacteria, viruses, and parasites that can cause disease in humans and other organisms.