Question

Assume that the population variance is unknown. We test the hypothesis that Ho: µ=5 against the one-sided alternative H1: µ≠5 at a level of significance of 5% and with a sample size of n=30. We calculate a test statistic = -1.699. The p-value of this hypothesis test is approximately ？ %. Write your answer in percent form. In other words, write 5% as 5.0.

Answer 1

Since population variance is unknown, the hypothesis test should be a t test

Hence, the test statistic is a t statistic

t = -1.699

degrees of freedom = n - 1 = 30 - 1 = 29

Since H1 : this is a two sided test

We find p-value using Excel function T.DIST.2t(t, df)

p-value = T.DIST.2t(1.699, 29)                     (For t.dist.2t we use positive t value)

p-value = 0.1

              = 10%

that is

p-value = 10                 (Answer as required in percent form)