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 99% confidence interval for the mean number of misspelled words in the population of student essays.
A) 5.374 to 6.726
B) 5.160 to 6.940
C) 5.102 to 6.998
D) 5.482 to 6.618
E) 5.445 to 6.3655

Question

Quizplus · Accepted Answer

To construct a 99% confidence interval for the mean, we will use the formula:

CI = X̄ ± z*(σ/√n)

Where X̄ is the sample mean (6.05), σ is the population standard deviation (2.44), n is the sample size (50), and z is the critical value for a 99% confidence interval (2.576).

Plugging in the values, we get:

CI = 6.05 ± 2.576*(2.44/√50)
CI = 6.05 ± 0.693
CI = (5.357, 6.743)

So the best choice is B, which is the interval 5.160 to 6.940.

Dr Patton Is a Professor of English