.2. 12, A chimpanzee named Sarah was the subject in a study of whether chimpanze

Question

.2. 12, 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 probleins and will thus pick the photo of the correct solution more often than a. Describe the parameter of interest in the context of this what would be done by random chance. study and assign a symbol to denote it. b. What is the observed value of the statistic in this case? c. Write out the null and alternative hypotheses for this first in words and then in symbols. d. 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 mull distribution, what is the p-value for the test? How did you calculate it? Probability of heads: 05 Nümber of tosses:8 Number of repetitions: 100 Animate Toss Coms Total 100

Explanation / Answer

Solution

Part (a)

Parameter of Interest:

Proportion, p of correct selection of photos. ANSWER 1

Part (b)

Observed value of ststistic: pcap = sample proportion = 7/8 = 0.875 ANSWER 2

Part (c)

Hypotheses:

In statistical terms:

Null H0: p = p0 = ½ Vs Alternative HA: p > ½ ANSWER 3

In physical terms

Sarah does not have any special skill to solve problem   vs Sarah has special skill to identify the related photos to solve problem. ANSWER 4

Part (d)

p-value here is the probability of getting 7 out 8 photos correct under the assumption (H0) that Sarah does not have any special skill to solve problem

= P(X ? 7). This is theoretically obtained using B(8, ½, 7 and 8).

But, here given the null distribution by way of the histogram of 100 tosses,

p-value = (3 + 1)/100 = 0.04 ANSWER 5

Part (e)

p-value of 0.04 => H0 is rejected at 5%, but accepted at 1% level of significance. So, there is enough, but not strong, evidence to suggest that Sarah has special skill to identify the related photos to solve problem. ANSWER 6

Part (f)

…….she would select 7 out of 8 photos correct is just 4% which is fairly low implying that the assumption (under H0) that Sarah does not have any special skill to solve problem is an unlikely event. ANSWER 7

Part (g)

A single dot represents 1% probability of selecting the correct photo even under no special skill to do so.

ANSWER 8

DONE

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