Question 981707: A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 48.96. Random sampling of 25 scores obtained from individuals who were bullied yielded a mean of 54.04 and a standard deviation of 11.49. (Use these numbers only for this question!)
Calculate the 99% confidence interval.
Steps:
As you know, two values will be required to complete the following equation:
_________ ≤ µ ≤ __________
For this question, what is the value that is below or less than µ?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! 1) Calculate the Margin of Error(ME)
ME = Z(alpha/2) * std.dev. / square root(n) where
Z(alpha/2) is the confidence coefficient = (1 - 0.99) / 2 = 0.005, now consult z table to find the corresponding value that goes with probability 0.005
z-value = -2.58
note that we ignore the - sign in the z-value
ME = 2.58 * 11.49 / square root(25) = 5.92884
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2) confidence interval(CI) = sample mean + or minus ME
CI = 54.04 + or - 5.92884, therefore
CI = 48.11116 < or = u < or = 59.96884
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3) The value that is below or less than µ is 48.11116
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