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.

Answer 1

Given that, sample size (n) = 20, sample mean = 41.0 and

sample standard deviation (s) = 3.7

The null and alternative hypotheses are,

H0 : μ = 35.0 (claim)

Ha : μ ≠ 35.0

This hypothesis test is a two-tailed test.

Since, population standard deviation is unknown we used t-test.

Test statistic is,

Test statistic = t = 7.252

Degrees of freedom = 20 - 1 = 19

Using t-table we get, t-critical values at 0.01 level of significance with 19 degrees of freedom are, tcrit = ±1.729

Decision Rule : Reject H0, if t > 1.729 or t < -1.729

Here test statistic = 7.252 is greater than 1.729, we reject the null hypothesis.

Conclusion : There is sufficient evidence to warrant rejection of the claim that the true mean score for all sober subjects is equal to 35.0.