Preliminaries This file should be in STAT240/homework/hw09 on your local computer. Download happiness_2019.csv and dc_weather.csv to STAT240/data . Problem 1 A one-sided hypothesis test of [H_A: eta_1 > 0] is performed on a linear model. The p-value of this test is 0.035. What would be the p-value if the same data was used to test the following alternatives? (a) [H_A: eta_1 < 0] Replace this text with your response. (b) [H_A: eta_1
eq 0] Replace this text with your response. Problem 2 Continue working with the happiness index vs GDP of countries model from Homework 8.
Build and interpret a 98% CI for the true slope of the linear relationship between happiness index and GDP. Does the interval cover 0?
Problem 3 Perform a hypothesis test of hypotheses [H_0: eta_1 = 0 quad ext{versus}quad H_A: eta_1
eq 0] for the slope of the happiness model. What is the test statistic, p-value, and conclusion at the 2% level?
Problem 4 How do the results of the hypothesis test in problem 3 relate to the results of the confidence interval in problem 2? Replace this text with your response. Problem 5 Which of the following conditions lead to a smaller standard error? Briefly explain your choices. A smaller sample size vs a larger sample size Replace this text with your response. A smaller value of (sigma) vs a larger value of (sigma) Replace this text with your response. Predicting closer to (ar{x}) vs predicting further from (ar{x}) Replace this text with your response. A smaller variance vs a larger variance in the original (X) data Replace this text with your response. Problem 6 Consider predicting the happiness index of a country with 1 GDP per capita. (a) Build a prediction interval for the happiness index of a new country with (x^* = 1) GDP per capita.
(b) Build a confidence interval for the height of the regression line at (x^* = 1).
Problem 7
(a) Make a plot of minimum temperature (in C) on the x axis versus dew point on the y axis. Comment on the shape of the data.
Problem 8 We want to test whether the slope of the linear relationship between minimum temperature and dew point is greater than 1. Write hypotheses corresponding to the question of interest and carry out the test on the weather data. Make a conclusion with (alpha = 0.05).
