In scanning electron microscopy photography, a specimen is placed in a vacuum chamber and scanned by an electron beam. Secondary electrons emitted from the specimen are collected by a detector and an image is displayed on a cathode ray tube. This image is photographed. In the past a 4 x 5 in camera has been used. It is thought that a 35-mm camera can obtain the same clarity. This type of camera is faster and more economical than the 4 x 5-in variety. (Based on a report entitled "Adaptation of a Thirty five Millimeter Photographic System for a Scanning Electron Microscope," E. A. Lawton, Biological Photography, volume 50, no. 3, July, 1982, p. 65.)
(a) Photographs of 15 specimens are made using each camera system. These unmarked photographs are judged for clarity by an impartial judge. The judge is asked to select the better of the two photographs from each pair. Let X denote the number selected taken by a 35-mm camera. If there is really no difference in clarity and the judge is randomly selecting photographs, what is the expected value of X?
(b) Would you be surprised if the judge selected 12 or more photographs taken by the 35-mm camera? Explain, based on the probability involved.
(c) If X _. 12, do you think that there is reason to suspect that the judge is not selecting the photographs at random?