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Compute the mean

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1) A test has the following properties: mean = 100, S.D. = 15, and r = .74. An individual has obtained a score of 85 on this test. Compute his or her SEM (standard error of measurement) and determine the scores that would be needed to develop a 95% confidence interval for this specific individual.

2) For the data listed below compute the mean, median, mode, S.D., Z scores for the scores 4 & 7, and t-scores for 1 & 3.

Raw scores 5, 4, 3, 7, 1, 3

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The solution addresses the following

1) A test has the following properties: mean = 100, S.D. = 15, and r = .74. An individual has obtained a score of 85 on this test. Compute his or her SEM (standard error of measurement) and determine the scores that would be needed to develop a 95% confidence interval for this specific individual.

2) For the data listed below compute the mean, median, mode, S.D., Z scores for the scores 4 & 7, and t-scores for 1 & 3.

Raw scores 5, 4, 3, 7, 1, 3

Solution Preview

1. M=100, SD=15, r=0.74
SEM=SD*SQRT(1-r)=15*SQRT(1-0.74)=7.65
we are adopting the normal distribution for our theoretical distribution of error, and the formula of the confidence interval is:
X + -z(0.975)*SEM
Where z(0.975)=1.96, because this is a two-tailed ...

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