1. (Use JMP)The data wine here provides the sample rating of wines selected from an online website from 2001 vintage. Here μ the average rating of the 2000 vintage, and we are interested in testing the hypotheses Ho: u 91.5 vs Hu>91.5
(a) Verify if the sample drawn is from a Normal population.
(b) Describe the critical region used to test the above hypotheses.
(c) What is the observed value of the test statistic?
(d) What is the distribution of the observed value of the test statistic?
(e) Based on the observed value and the critical region what is your final decision?
(f) Find the p-value to test the above hypotheses.
(g) Based on the p-value (given a=0.05) what is your final decision
(h) Are the answers in (g) and (e) consistent?
(i) Construct a 99% CI using JMP
(j) Using the above CI test the hypotheses Hoμ= 91.5 vs H1: μ 91.5.
(k) Calculate the power of the test when u = 93
(1) Calculate the power of the test when u = 300, for which value of u would the power of the test be equal to 1.
(m) Continuation of part (b): what will be the power of the test for u = 93 if we do not change the sample sd but keep increasing the sample size arbitrarily.
2. If the airline flight that you are on is 20 minutes late departing, can you expect the pilot to make these minutes up by flying faster than usual? The data summarizes the status of a sample of 1050 flights during August 2015. (Use the data set Flight)
(a) Do you expect the number of minutes that the flight is delayed departing to be associated with the arrival delay? Answer this question based on your understanding of the situation and without exploring the data.
(b) Make a scatterplot of the arrival delay (in minutes) on the departure delay (also in minutes). Summarize the association present in the scatterplot if any. Draw the histogram borders and don't forget to mention the presence of outliers if you find one. (Provide JMP output)
(c) Find the correlation between arrival delay and departure delay. (Provide JMP output)
(d) How is the correlation affected by the evident outlier, a flight with very long delays? (e) How would the correlation change if delays were measured in hours rather than minutes? (f) Draw the regression line and write down its equation. (Provide JMP output)
(g) What is the RMSE of the above regression equation (see the JMP output)
(h) What is the R2 of the above regression equation? How is it related to the correlation coefficient which you had calculated earlier?
(i) While testing Ho: Bo=0 vs H1: Bo 0 what is the observed value of the test statistic and based on the p-value what is your final decision?
(j) While testing Ho: B1-0 vs H1: B10 what is the observed value of the test statistic and based on the p-value what is your final decision?
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