Suppose the preliteracy scores of three-year-old students in the United States are normally distributed. Shelia, a preschool teacher, wants to estimate the mean score on preliteracy tests for the population of three-year-olds. She draws a simple random sample of 20 students from her class of three-year-olds and records their preliteracy scores (in points).

81,84,87,91,91,91,92,92,94,95,97,99,100,102,106,107,107,111,115,116

Calculate the sample mean (x), sample standard deviation (), and standard error (SE) of the students' scores.

x= ___________________(Round to 4 decimal places)

= ___________________(Round to 4 decimal places)

SE= ___________________(Round to 4 decimal places)

Determine the -critical value () and margin of error () for a 99% confidence interval.

= ______________________(Round to 3 decima places)

= ________________________(Round to 3 decimal places)

What are the lower and upper limits of a 99% confidence interval?

Round your answers to three decimal places.

lower limit: __________________________(Round to 3 decimal places)

upper limit: ______________________(Round to 3 decimal places)

Which is the correct interpretation of the confidence interval?

A)There is a 99% chance that the true population mean is between 92.171 points and 103.629 points.

B)There is a 99% chance that the population mean is between 91.537 points and 104.263 points.

C)Shelia is certain that the true population mean is between 91.537 points and 104.263 points.

D)Shelia is 99% confident that the true population mean is between 92.171 points and 103.629 points.

E)Shelia is 99% confident that the true population mean is between 91.537 points and 104.263 points.