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1. QUESTION

WITH USERNAME: [email protected] KEY: [email protected] (only for the exercise, when logged in, click e-book, all the questions start with 6.xxx are in ch6 under 6g. And question 7, 26 is under ch7 >> 7b >>7.1 exercise. The website is just for the questions(and data), no actions need to be done on the website and follow the instructions below.

Create a title page that includes your student number.
Complete Exercise 6.119. Create the plot by hand using a ruler and label both the x- and y-axis. Please write legibly. The y-axis should be ‘% Hit’ and you can use whatever sample size (n) you like. Provide the sample size (n) in your answer and use the same sample size (n) for 6.120.
Complete Exercise 6.120. Create the plot by hand using a ruler and label both the x- and y-axis. Please write legibly and compare your results with Exercise 6.119.
Import ENDOW.gtd into gretl. Complete Exercise 7.26 using an alpha level of 0.05. You can use gretl to perform calculations. To achieve full grades document the four common steps for tests of significance (refer to page 325).
Save Part B as a pdf document and upload to the UM Learn Dropbox Assignment 5 – Part B.

[Note: The pdf you submit should include all of Assignment 5 – Part B. The pdf will have multiple pages, with the first being a title page.]

Subject Pages Style Statistics 5 APA

Coverage Interval for Confidence Interval

95% Confidence Interval Percentage Coverage

Fig 1: 95% Confidence interval coverage percent

With the sample size n=40, the percentage coverage for 95% confidence level,  the percent of intervals including the population mean in various confidence intervals vary significantly. While the average hits (percent of intervals including the population mean) in the 200 sampled confidence intervals is 94% (which is close to the 95% confidence level used in the simulation), the variation is especially below the 95% baseline after 30 intervals onwards. Thus the simulation supports the assertion that the standard CI of the mean has 95% coverage when a sample is drawn from a normal population.

90% Confidence Interval Percentage Coverage

At 90% confidence level, n=40, the simulation of percentage coverage of the sampled 200 intervals shows that they are progressively above 90% with the coverage hitting baseline (90%) at 50 and 60 confidence intervals and not lesser. The percentage hits range between 90% and 97% with an empirical coverage of 93%. Thus the simulation supports the assertion that the standard CI of the mean is likely to be higher than 90% coverage when a sample is drawn from a normal population.

Fig 2: 90% Confidence interval coverage percent

Comparison of 90% and 95% Coverage Percentages (n=40)

Empirically, it is likely that for the 200 confidence intervals sampled, the population mean will be covered on probability between 90% and 95%.  However, for intervals between 10 and 30, the coverage is similar for both confidence levels.

Fig 3: Comparison of 90% and 95% Coverage Percentages

Investigating Endowment Effect

To test the hypothesis that there is no difference between the two prices (maximum buying price and minimum selling price), the means µ1 (mean for maximum buying price) and µ2 (mean for minimum selling price) are compared.

H0: µ1 = µ2

H1: µ1 ≠ µ2

At 95% confidence level, the results are t(78) = -2.94147, p= 0.004299 < 0.05. Therefore, reject the null hypothesis. There is no sufficient evidence in the data at 95% confidence to indicate that the means between the two prices are not different.

Further, to examine the variation the statistics indicate that Mean for Maximum Buying Price = 3.58725 which is way lesser than that of Minimum Selling Price which is 5.175.

Therefore, it is conclusive that the students are willing to sell at a minimum price higher than the maximum price they are willing to buy the Vosges Woolloomooloo gourmet chocolate bar made with milk chocolate and coconut.

The 95% confidence interval for mean of endowment effect is: 1.00938 to 2.16612

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