STAT 218 HW 5

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Statistics

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Feb 20, 2024

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Homework 5 Total : 43 Name: Jordan Wattles 1. Comment on the scatterplot below in terms of direction, form, and strength, AND whether they meet the validity conditions for a regression. (4 pts ) its direction is positive; the form is approximately linear; strong; no real outliers 2. The regression analysis was intended to predict an area’s cirrhosis death rate based on the area’s liquor consumption per capita. a) Comment on the direction, form, and strength of the scatterplot. Circle any outliers (4 pts) Direction: positive Form: approx. linear Strength: moderate to strong b) What statistical measure can confirm your visual assessment above in terms of direction and strength AND WHY ? (2 pts) Least square regression c) Do these data meet the validity conditions for a simple linear regression? List the conditions (2 pts) Yes, it is approx. linear, approx. the same distribution and variability is approx. consistent

d) Interpret the R-squared value in the context of the problem (3 pts) 46.% of the variation in cirrhosis death rate is determined by liquor consumption e) Label the relevant terms in the regression table with one of the following ( b 0 ,b 1 ) (2 pts) B 1 = 21.96 B 0 = .7222 f) Write the null and alternative hypotheses in words and in symbols (4 pts) Null: there is no linear association between cirrhosis death rates and the amount of liquor consumed per capita H 0 : B = 0 Alternative: there is a linear association between cirrhosis death rates and the amount of liquor consumed per capita H a : B ≠ 0 g) Interpret the 95% confidence interval (2 pts) We are 95% confidence the true LRP of linear association between cirrhosis death rates and liquor consumption per capita is between (.4869, .9576) h) Make a decision regarding the null hypothesis. Justify your decision with the standardized statistic, the p-value, AND the confidence interval (4 pts) Reject the null due to the confidence interval not capturing the value 0, the p-value being less .05, and the standardized stat of 1.193 are significant to say there is linear association. 3. The counts of insects in agricultural experimental units are treated with different insecticides. Data has been collected on 6 insecticides and a visual display of the data is below. a) Comment on the boxplots and what you may expect to see before looking at the formal statistics ( 2 SENTENCES MAX ) (1 pt) Sprays A, B and F have the highest averages, while C, D and E had lower averages. Sprays A, B, and F also had wider ranges than the other 3. b) Write the null and alternative hypothesis IN WORDS AND SYMBOLS (6 pts) Null: the LRA insects affected is the same for all of sprays H 0 : u a = u b = u c = u d = u e = u f

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