When one experiences a lack of control in one's life, does one compensate by seeking structure elsewhere? Assign 36 undergraduate students to one of two conditions. All are asked to identify a concept associated with a series of "grainy" pictures that contain an embedded image and are presented to them sequentially. During the task they can ask questions to help them determine the associated concept. Half of the subjects (the lack-of-control group) receive feedback that is random and noncontingent on their questions. The other half receive useful feedback (the in-control group). After attempting to complete the task, all subjects are presented with 12 grainy pictures that are similar to those used in the task but lack embedded images. All are asked whether they perceive an image in the pictures, and the number of pictures identified as containing an image is counted for each subject. Here are the summary statistics:
Lack of control group (size: 18) (Mean: 5.16) (Standard Deviation: 3.5)
In control group (size: 18) (Mean: 3.47) (Standard Deviation: 2.0)
(a) What degrees of freedom would you use in the conservative two-sample t procedures to compare the lack-of-control and in-control groups?
(b) What is the two-sample t test statistic for comparing the mean number of pictures identified as having an image for the two groups?
(c) Test the null hypothesis of no difference between the two population means against the two-sided alternative. Use your statistic from part (b) with degrees of freedom from part (a). Accept or Reject the null hypothesis and explain.