Question

Part I - Do Students Really Cheat? (30%)

In a recent poll 400 students were asked about their experiences with witnessing academic dishonesty among their classmates. Suppose 172 students admitted to witnessing academic dishonesty, 205 stated they did not and 23 had no opinion. Use the sign test and a significance of 0.05 to determine whether there is a difference between the number of students that have witnessed academic dishonesty compared to those that have not.

Answer 1

The sign test is a statistical method to test for consistent difference between pairs of observation. Given pairs of observations ( such as weight pre and post treatment ) for each subject, the sign test determines if one member of the pair (such as pre-treatment ) tends to be greater than (or less than ) the other member of the pair (such as post treatment).

First of all, we set up the Hypothesis-

H_{​​​​​​0:} There is no difference between number of students that have differenced academic dishonesty compared to those who have not.

H_{​​​​​​1:} There is difference between number of students that have differenced academic dishonesty compared to those who have not.

The sign test is a non- parametric test which makes very few assumptions about the nature of the distributions under test- this means that it has very general applicability but may lack the Statistical power of the alternative tests.

Preferred A - Students admitted to witnessing dishonesty. (=172)

Preferred B - Students not admitted to witnessing dishonesty.

(=205)

No Preference - Number of ties.(=23)

p-value is 0.05 and z value is 24.286323

Which implies that p value is less than the z value, Hence null hypothesis is rejected and we may conclude that there is a difference between the number os students that have experienced academic dishonesty as compared to those who have not.