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Explain what value or values for c make the equation x x c have one and only

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two objects and recorded whether or not the dog being tested correctly chose the object indicated. A four-year-old male beagle named Augie participated in this study. He chose the correct object 42 out of 70 times when the experimenter leaned towards the correct object. (a) (2 points) Let the parameter of interest, π, represent the probability that the long-run probability that Augie chooses correctly. Researches are interested to see if Augie understands human body cues (better than gussing). Fill in the blanks for the null and alternative hypotheses. H0 : Ha : (b) (6 points) Based on the above context, conduct a test of significance to determine the p-value to investigate if domestic dogs understand human body cues. What conclusion will you draw with significance level of 10%? (If you use an applet, please specify which applet you use, and the inputs.) (c) (5 points) Based on the above context, conduct a test of significance to determine the p-value to investigate if domestic dogs understand human body cues. What conclusion will you draw with significance level of 5%? (If you use an applet, please specify which applet you use, and the inputs.) (d) (2 points) Are your conclusions from part (b) and (c) the same? If they are different, please provide an explanation. (e) (5 points) Shown below is a dotplot from a simulation of 100 sample proportions under the assump- tion that the long-run probability that Augie chooses correct is 0.50. Based on this dotplot, would a 90% confidence interval for π contain the value 0.5? Explain your answer. (f) (4 points) Compute the standard error of the sample proportion of times that Augie chose the object correctly. 1 (g) (5 points) (h) (3 points) question? (i) (4 points) (j) (4 points) A. B. C. Construct an approximate 95% confidence interval for π using the 2SD method. What is the margin of error of the confidence interval that you found in the previous How would you interpret the confidence interval that you found in part (g)? Which of the following is a correct interpretation of the 95% confidence level? If Augie repeats this process many times, then about 95% of the intervals produced will capture the true proportion of times of choosing the correct objective. About 95% times Augie chooses the correct objective. If Augie repeats this process and constructs 20 intervals from separate independent sam- ples, we can expect about 19 of those intervals to contain the true proportion Augie chooses the correct objective. (k) (4 points) object 21 out of 35 times. Conjecture how, if at all, the center and the width of a 99% confidence interval would change with these data, compared to the original 2SD 95% confidence interval. The center of the confidence interval would . The width of the confidence interval would . (l) (4 points) Suppose that we repeated the same study with Augie, and this time he chose the correct object 17 out of 35 times, and we also change the confidence level from 95% to 99%. Conjecture how, if at all, the center and the width of a 99% confidence interval would change with these data, compared to the original 2SD 95% confidence interval. Suppose that we repeated the same study with Augie, and this time he chose the correct The center of the confidence interval would The width of the confidence interval would . .
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van and Alex, have the same productivities: Sylvan is identical to Rajan, while Alex and Esther are identical. Esther and Rajan both engage in market work. Sylvan works full time at home, so only Alex works in the market. a) Given this information, which couple has the higher opportunity cost of home produced goods? Explain how you determined this. You can add a diagram if that helps, but you are not required to include one. b) Can you determine which couple has the higher utility? Explain why or why not. Suppose now that value of market production for both Alex and Esther increased to \$12/per hour. c) Explain the change in the household joint production possibility frontier generated by this change. d) Explain what would happen to each couple’s choice of both household and market produced goods, using an analysis by means of income and substitution effects. e) What changes in time allocation for each couple that would be necessary to produce and consume this new bundle? Briefly explain your reasoning.
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