Dr. Patton is a professor of English. Recently she counted the number of misspelled works in a group of student essays. She noted the distribution of misspelled words per essay followed the normal distribution with a standard deviation of 2.44 words per essay. For her Tuesday class of 50 students, the mean number of misspelled words per essay was 6.05. Construct a 95% confidence interval for the mean number of misspelled words in the population of student essays.
A) 5.374 to 6.726
B) 5.161 to 6.939
C) 5.102 to 6.998
D) 5.482 to 6.618
E) 5.445 to 6.3655

Question

Quizplus · Accepted Answer

The 95% confidence interval for the mean number of misspelled words can be calculated using the formula for the confidence interval of the mean with known standard deviation and sample size: $\bar{x} \pm z \frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the z-score corresponding to the confidence level (for 95%, $z = 1.96$), $\sigma$ is the standard deviation, and $n$ is the sample size. Plugging in the given values ($\bar{x} = 6.05$, $\sigma = 2.44$, $n = 50$), we get the confidence interval as 5.374 to 6.726.

Dr Patton Is a Professor of English