Question

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). 74,79,83,85,88,90,94,95,95,97,99,99,100,103,105,105,106,107,107,108

Calculate the sample mean (?⎯⎯⎯x¯), sample standard deviation (?s), and standard error (SE) of the students' scores. Round your answers to four decimal places.

Determine the ?t-critical value (?t) and margin of error (?m) for a 95% confidence interval. Round your answers to three decimal places.

What are the lower and upper limits of a 95% confidence interval? Round your answers to three decimal places.

x¯=

?=

?=

SE

? =

lower limit:

upper limit:

Answer 1

Sample mean = x̅ = 95.95

Sample size = n = 20

Sample S.D = s = 10.0025

Confidence Level = 95

Significance Level = α = (100-95)% = 0.05

Degrees of freedom = n-1 = 20 -1 = 19

Critical value = t* = 2.093   [ using Excel =TINV(0.05,19) ]

Standard Error = s/√n = 10.0025/√20 = 2.2366

m = Margin of Error = t*(s/√n )= 2.093*2.2366 = 4.681

Lower Limit = x̅ - Margin of Error = 95.95 - 4.6812 = 91.269

Upper Limit = x̅ + Margin of Error = 95.95 + 4.6812 = 100.631