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

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 58 students results in 5 who fail the test.

A) $p > 0.039$
B) $p < 0.133$
C) $\mathrm { p } < 0.147$
D) $p < 0.039$