4 A test of sobriety involves measuring the subjects motor s

4) A test of sobriety involves measuring the subject\'s motor skills. Twenty randomly selected sober subjects take the test and produce a mean score of 41.0 with a standard deviation of 3.7. At the 0.01 level of significance, test the claim that the true mean score for all sober subjects is equal to 35.0. Use the traditional method of testing hypotheses.

Solution

x = 41.0

s= 3.7

mu = 35.0

alpha= 0.01

critical value for 0.01 two tailed t-tes with dof 19 = 2.861

test statistics= (x-mu)/(sigma/sqrt(n)) =(41.0-35.0)/(3.7/sqrt(20)) = 7.25

since, test statistics is greater than critical value, we can reject the claim mean score for all is 41.0