252HW4-2018 Winter-Questions.pdf

# 252HW4-2018 Winter-Questions.pdf - Stat 252 Homework 4...

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Stat 252 Homework # 4 Questions Winter 2018 1 STAT 252 Homework 4 (63 marks) Due Friday, April 6 by 5pm For questions that state “ SHOW ALL STEPS ”, write all the steps of a hypothesis test or confidence interval as indicated below. For other questions that say do “ NOT ” show all steps, read the ques tion carefully and follow the exact instructions regarding what is required. Whenever you are asked to “ carry out the most appropriate test ” and “SHOW ALL STEPS” : i) Select the most appropriate hypothesis test and define the parameter(s) of interest. ii) State clearly the null and alternative hypothesis in terms of the parameter(s). iii) Calculate the test statistic, being sure to state its components. iv) Calculate df . Determine the P -value for the test AND state the strength of the evidence against H 0 . State whether P is less than or greater than alpha and, based on this comparison, decide whether to reject or not reject H 0 . If the exact P -value is given in output, then report it as is. If not, then you must estimate the P -value (within a range of values) using the appropriate statistical table. v) Based on the research problem and referring to the significance level given, write a conclusion in words. Whenever you are asked to calculate a “ confidence interval ” and “ SHOW ALL STEPS : i) State the critical value of the test statistic. ii) Calculate the confidence interval, showing calculations of all its components. iii) Interpret the interval. Note: If you need to use the t-table or F-table and the degrees of freedom you need are NOT on the table, round your degrees of freedom DOWN to the nearest one. 1. (Eight parts; 33 marks in total) A study was conducted with the objective of increasing muzzle velocity of mortar-like antipersonnel weaponry with grenade-type golf-ball-size ammunition. Some researchers determined that the addition of an O-ring can reduce propellant gas escape in the muzzle and increase muzzle velocity. Three explanatory variables were considered in the study: vent hole volume (in cubic inches), the presence of an O - ring (with or without), and discharge hole area (in inches) which might affect the pressure pulse of propellant gases. The researcher measured the muzzle velocity 8 times for each combination of the four levels of discharge hole area (0.016, 0.03, 0.048, and 0.062) as well as with or without an O-ring, for a total of 64 observations. In each trial, vent hole volume was also observed. For parts (a) (e): (No output is required for these parts) Consider the regression model below (which will be referred to as the “ original model ” for parts (a) – (e)) for average muzzle velocity given the variables, volume , ring , and area

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