a sample of n = 20 scores has a mean of M = 30. a. if the sample standard deviat

Question

a sample of n = 20 scores has a mean of M = 30. a. if the sample standard deviation is s = 10, would a scoreof X = 38 be considered an extreme value (out in the tail of thedistribution)? b. if the sample standard deviation is s = 2, would a score ofX = 38 be considered an extreme value (out in the tail ofdistribution)? a sample of n = 20 scores has a mean of M = 30. a. if the sample standard deviation is s = 10, would a scoreof X = 38 be considered an extreme value (out in the tail of thedistribution)? b. if the sample standard deviation is s = 2, would a score ofX = 38 be considered an extreme value (out in the tail ofdistribution)?

Explanation / Answer

= 30
n = 20 a)   X = 38
= 10
Ho : score of X = 38 be considered an extreme value
H1: score of X = 38 not be considered an extreme value
standard error, m = / n = 10/ 20 =2.236 ( X - ) / m = ( 38- 30)/ 2.236)
hence Z = 3.58 critical value of z for  two-tail test at the 0.01level = 2.58 since Z is more than critical z, hence we reject thehypotheses hence score of X = 38 not be considered an extremevalue
b)X = 38
= 2
Ho : score of X = 38 be considered an extreme value
H1: score of X = 38 not be considered an extreme value
standard error, m = / n = 2/ 20 =0.447 ( X - ) / m = ( 38- 30)/ 0.447)
hence Z = 17.89 critical value of z for  two-tail test at the 0.01level = 2.58 since Z is more than critical z, hence we reject thehypotheses hence score of X = 38 not be considered an extremevalue

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