Question

A recent study investigated whether vodka is less likely to give you a hangover than wine. Twenty participants on a night out were asked to drink only vodka for the whole evening then rate how they felt the next day out of 10 (0 = I feel fantastic, 10 = I can't move my head in case it explodes). The following month, they were asked to do the same again, only this time they were asked to drink only white wine. The t-score was 2.56. Which of the sentences below is correct?

It is significant at the 1% level with a two-tailed test.

It is not significant with a one-tailed test.

It is not significant with a two-tailed test.

It is significant at the 5% level but not the 1% level with a two-tailed test.

Answer 1

We have given,

sample size n = 20, calculated t score = 2.56

Since here we have data like pre and post experiment, we had used two tailed paired t test to get t score = 2.56

now we have to compute critical values of t for level of significance 1% and degrees of freedom = n-1 = 19 using the t distribution table which is 2.861

Since our calculated value 2.56 falls between -2.861 and 2.861, hence we failed to reject the null hypothesis at 1% level of significance

now we have to compute critical values of t for level of significance 5% and degrees of freedom = n-1 = 19 using the t distribution table which is 2.093

Since our calculated value 2.56 doesn't fall between -2.093 and 2.093, hence we reject the null hypothesis at 5% level of significance

Therefore the correct option is

It is significant at the 5% level but not the 1% level with a two-tailed test.