A chimpanzee named Sarah was the subject in a study of whether chimpanzees can s

Question

A chimpanzee named Sarah was the subject in a study of whether chimpanzees can solve problems. Sarah was shown 30-second videos of a human actor struggling with one of several problems (for example, not able to reach bananas hanging from the ceiling). Then Sarah was shown two photographs, one that depicted a solution to the prob- lem (like stepping onto a box) and one that did not match that scenario. Researchers watched Sarah select one of the photos, and they kept track of whether Sarah chose the cor- rect photo depicting a solution to the problem. Sarah chose the correct photo in seven of eight scenarios that she was presented. We want to run a test of significance to determine whether Sarah understands how to solve problems and will thus pick the photo of the correct solution more often than what would be done by random chance. a. b. c. d. e. f. g. Describe the parameter of interest in the context of this study and assign a symbol to denote it. What is the observed value of the statistic in this case? Write out the null and alternative hypotheses for this first in words and then in symbols. We conducted a test of significance using the One Pro- portion applet and got the following null distribution for the “number of heads.” (Note: this null distribution uses only 100 simulated samples and not the usual 1,000 or more.) Based on the null distribution, what is the p-value for the test? How did you calculate it? Based on your p-value, do you have strong evidence that Sarah understands how to solve problems similar to those she was presented? How are you deciding? Justify. Complete this sentence describing what the p-value means: If Sarah doesn’t understand how to solve prob- lems and is just guessing at which picture to select, the probability she would ... What does a single dot in the null distribution represent in terms of Sarah and the photos?

Explanation / Answer

Part (a) : The parameter of interest is : The probability that Sarah correctly solves the problems similar to those she was presented. Let's denote this parameter with P.

Part (b) : The statistics used in this case is the Proportion of times when Sarah correctly solves the problem similar to those she was presented. The observed value of this statistic is (7/8) = 0.875 .

Part (c) : Null hypothesis : The probability that Sarah correclty solves the problems similar to those she was presented is 0.5         In symbols:      H0 : P=0.5

Alternate Hypothesis: The probability that Sarah correctly solves the problems similar to those she was presented is strictly greater than 0.5.   In symbols: Ha : P>0.5

Fpr answers to Part (d) to (g); Please provide the null distribution obtained using One proportion applet.Only after this, remainin parts can be answered.

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