Question

The p-value is greater than the significance level.

(a) We can have a Type I error

(b) The absolute value of the test statistic is less than the absolute value of the t critical value

(c) If we had used a larger value for alpha the p-value would have been smaller

(d) We must have had a two tail test

Answer 1

(b) The absolute value of the test statistic is less than the absolute value of the t critical value.

We know the decision rule in terms of p-value and critical value are given as below:

We reject the null hypothesis when the p-value is less than the alpha value or level of significance and we do not reject the null hypothesis when the p-value is greater than the alpha value.

We reject the null hypothesis when the absolute test statistic value is greater than the absolute critical value, and we do not reject the null hypothesis when the absolute test statistic value less than the critical value.