8. Performance scores on a motor skills task form a normal distribution with = 2

Question

8. Performance scores on a motor skills task form a normal distribution with = 20 and = 4.

A psychologist is using this task to determine the extent to which increased self-awareness affectsperformance. The prediction for this experiment is that increased self-awareness will reduce a subject’s concentration and result in lower performance scores. A sample of N = 16 subjects is obtaine

d, and each subject is tested on the motor skills task while seated in front of a large mirror. The purpose of the mirror is to make the subjects more self-aware. The mean score for this sample is sample mean = 15.5. Do a one-tailed z test with = .05 to test the psychologist’s prediction (include all elements as detailed in z-Test Handout).

Explanation / Answer

The population parameters are mean= 20 and sd =4,

the sample mean is given to be 15.5

One tailed Z test is calculated as= (sample mean-pop mean)/ sd

=(15.5-20)/4

= -1.125, taking abs value we get test statistic as 1.125,

Zalpha, where alpha takes value 0.05 is 1.645,

since our null hypothesis is accepted and we conclude that psychologist's prediction is correct.

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