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
1. Calculate the sample mean (x⎯⎯⎯), sample standard deviation (), and standard error (SE) of the students' scores. Round your answers to four decimal places.
2. Determine the -critical value () and margin of error (m) for a 99% confidence interval. Round your answers to three decimal places.
3. What are the lower and upper limits of a 99% confidence interval? Round your answers to three decimal places.
4. Which is the correct interpretation of the confidence interval?
a. Shelia is certain that the true population mean is between 91.537 points and 104.263 points.
b. Shelia is 99% confident that the true population mean is between 92.171 points and 103.629 points.
c. There is a 99% chance that the true population mean is between 92.171 points and 103.629 points.
d. Shelia is 99% confident that the true population mean is between 91.537 points and 104.263 points.
e. There is a 99% chance that the population mean is between 91.537 points and 104.263 points.