Question

statistic question

Perform the following hypothesis test using the critical-value approach.

A test of sobriety involves measuring the subject's motor skills. The mean score for men who are sober is known to be 35.0. A researcher would like to perform a hypothesis test to determine whether the mean score for sober women differs from 35.0. Twenty randomly selected sober women take the test and produce a mean score of 41.0 with a standard deviation of 3.7. Perform the hypothesis test at the 1% significance level. Remember to interpret your answer within the context of the problem.

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

Ha : μ ≠ 35.0

Test statistic is,

=> Test statistic = t = 7.252

Degrees of freedom = 20 - 1 = 19

Using t-table we get, t-critical values at significance level of 0.01 with 19 degrees of freedom are, t​​​​​​crit = ± 2.861

Decision Rule : Reject H0, if t < -2.861 or t > 2.861

Since, test statistic = t = 7.252 is greater than 2.861, we reject the null hypothesis.

Conclusion : There is sufficient evidence to conclude that the mean score for sober women differs from 35.0.