Assume that a simple random sample has been selected from a normally distributed

Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses test statistic, critical value(s) or P-value (or range of P-values) as appropriate and state the final conclusion that addresses the original claim. 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.

Explanation / Answer

Hypothesis:

Ho: u = 35

Ha: u !=35

critical values z = -2.58 , 2.58

reject null hypothesis if Z<-2.58 or z > 2.58

=>

test static = x-mean/std/sqrt(n)

= 41-35/3.7/sqrt(20)

= 7.252

hence reject null hypothesis

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