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one hundred teachers attended a seminar on mathematical problem solving. The att

ID: 3170391 • Letter: O

Question

one hundred teachers attended a seminar on mathematical problem solving. The attitudes of representative sample of 12 of the teachers were measured before and after the seminar. A positive number for change in attitude indicates that a teacher's attitude toward math became more positive. The twelve change scores are as follows. E Part (a) What is the mean change score? (Round your answer to two decimal places) E Part (b) What is the standard deviation for this sample? (Round your answer to two decimal places.) E Part (c) What is the median change score? (Round your answer to one decimal place.) E Part (d) Find the change score that is 2.2 standard deviations below the mean. (Round your answer to one decimal place)

Explanation / Answer

Calculating the sample mean, also called average, point estimate, or expected value. ( - mu)
= (1/n)xi
= (1/12)(4 + 8 - 1 + 1 + 0 + 4 - 2 + 2 - 1 + 5 + 4 - 3)
= (1/12)(21)
= 21/12
= 1.75

Calculating the standard deviation (lower case sigma, upper case)(note n-1)
= [1/(n-1)*(xi-)^2]
= {[1/(12-1)][(4-1.75)^2 + (8-1.75)^2 + (-1-1.75)^2 + (1-1.75)^2 + (0-1.75)^2 + (4-1.75)^2 + (-2-1.75)^2 + (2-1.75)^2 + (-1-1.75)^2 + (5-1.75)^2 + (4-1.75)^2 + (-3-1.75)^2]}
= [(1/11)(120.25)]
= (120.25/11)
= 10.93
= 3.3

The change score
= 1.75 - 2.2*3.3
= 1.75 - 7.26
= -5.51