Researchers constructed two test sheets, each sheet including 20 photos of the faces of dog–owner pairs taken at a dog lovers' field festival. The 20 sets of dog–owner pairs on the two sheets were equivalent with respect to breed, diversity of appearance, and gender of owners. On the first sheet, the dogs were matched with their owners, while on the second sheet, the dogs and owners were deliberately mismatched. Three experiments were conducted, and in all experiments, subjects were asked to "choose the set of dog–owner pairs that resemble each other, Sheet 1 or Sheet 2," and were simply told the aim of the research was a "survey on dog–owner relationships." In the first experiment, the original sheets were shown to subjects; in the second experiment, just the "mouth region" of the owners was blacked out in all the pictures on both sheets; in the third experiment, just the "eye region" of the owners was blacked out. Subjects were assigned at random to the three experimental groups, and in each experiment, the number of subjects who selected the sheet with the dogs and their owners correctly matched was recorded. Experimenters were interested in whether blacking out portions of the face reduced the ability of subjects to correctly match dogs and owners. The results are given in the table. Experiment Number of subjects Number correctly matched 1 61 49 2 (mouth blacked out) 51 37 3 (eyes blacked out) 60 30 SOLVE: Assume the samples can be thought of as an SRS. A hypothesis test can be conducted given that there are more than five successes (correctly identified the pairs) and more than five failures in each sample. Calculate the sample proportion for each group, ?̂ 1 and ?̂ 2, and the pooled sample proportion ?̂ . Give your answers to four decimal places. Computer the test statistic z. Give your anwer to four decimal places.
Researchers constructed two test sheets, each sheet including 20 photos of the faces of dog–owner pairs taken at a dog lovers' field festival. The 20 sets of dog–owner pairs on the two sheets were equivalent with respect to breed, diversity of appearance, and gender of owners. On the first sheet, the dogs were matched with their owners, while on the second sheet, the dogs and owners were deliberately mismatched. Three experiments were conducted, and in all experiments, subjects were asked to "choose the set of dog–owner pairs that resemble each other, Sheet 1 or Sheet 2,"
and were simply told the aim of the research was a "survey on dog–owner relationships."
In the first experiment, the original sheets were shown to subjects; in the second experiment, just the "mouth region" of the owners was blacked out in all the pictures on both sheets; in the third experiment, just the "eye region" of the owners was blacked out. Subjects were assigned at random to the three experimental groups, and in each experiment, the number of subjects who selected the sheet with the dogs and their owners correctly matched was recorded. Experimenters were interested in whether blacking out portions of the face reduced the ability of subjects to correctly match dogs and owners. The results are given in the table.
| Experiment | Number of subjects | Number correctly matched |
| 1 | 61 | 49 |
| 2 (mouth blacked out) | 51 | 37 |
| 3 (eyes blacked out) | 60 | 30 |
SOLVE: Assume the samples can be thought of as an SRS. A hypothesis test can be conducted given that there are more than five successes (correctly identified the pairs) and more than five failures in each sample.
Calculate the sample proportion for each group, ?̂ 1 and ?̂ 2, and the pooled sample proportion ?̂ . Give your answers to four decimal places.
Computer the test statistic z. Give your anwer to four decimal places.
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