Suppose you are testing to see if your dog, Hope, understands pointing towards an object. You put Hope through 20 trials and 12 times (or 60%) she goes to the correct object when given a choice between two objects. You then conduct a test of significance and generate the following 100 simulations using an applet.

a. Write out the null and alternative hypotheses for this study in words.
b. If we let π be the long-run proportion of times Hope will go to the correct object, write out the null and alternative hypotheses for this study in symbols.
c. Based on the null distribution shown, what is the p-value for your test?
d. Based on your p-value, do you have strong evidence that Hope understands pointing?
e. Using the null distribution shown, what is the smallest proportion of times Hope could go toward the correct object so that you would have strong evidence that she understands pointing toward an object?
f. Which of the following best describes what a single dot represents in the null distribution shown?

i. One possible value of the proportion of times Hope goes to the correct object out of 20 if she goes to the correct object 50% of the time in the long run

ii. One possible value of the proportion of times Hope goes to the correct object out of 20 if she goes to the correct object more than 50% of the time in the long run

Transcribed Image Text:

Probability of heads: 0.5 20 Number of tosses: 100 Number of repetitions: M Animate Toss Coins Total = 100 18 12 8.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 Proportion of heads