A one-sided confidence interval for $\mathrm { p }$ can be written as $p \hat { p } - \mathrm { E }$ where the margin of error $\mathrm { E }$ is modified by replacing $z _ { \alpha / 2 }$ with $z _ { \alpha }$. 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) $p

Question

A one-sided confidence interval for $\mathrm { p }$ can be written as $p < \hat { p } + \mathrm { E }$ or $p > \hat { p } - \mathrm { E }$ where the margin of error $\mathrm { E }$ is modified by replacing $z _ { \alpha / 2 }$ with $z _ { \alpha }$. 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) $p < 0.062$ B) $p < 0.154$ C) $p > 0.062$ D) $p < 0.167$

Quizplus · Accepted Answer

To construct a one-sided confidence interval with 90% confidence, we use $z_{0.10}$ for the margin of error. The sample proportion $\hat{p} = \frac{8}{74} \approx 0.108$. Using $z_{0.10} \approx 1.28$, the margin of error $E = z_{0.10} \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$. Calculating this gives $p < 0.154$.

A One-Sided Confidence Interval For p\mathrm { p }p Can Be Written As

A One-Sided Confidence Interval For $\mathrm { p }$ Can Be Written As