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John works as a "sanitation engineer" for a zoo that has only 10 elephants and 8 zebras in the whole zoo (a budgetary problem). Every day he goes to work he feels like he is shoveling a great deal of waste and he wants to know if the amount of waste that he disposes of on average is different than the normal amount elephant/zebra zoos dispose of. On any given day 1500 pounds of waste, with a standard deviation of 500 pounds, are removed from these types of facilities across the country, however John shovels 1700 pounds of waste a day. Is John shoveling significantly more crap than the average facility? State Null Hypothesis ho:μ 1500 Alternative Hypothesis h₁:μ Decide on a (usually .05) a = Decide on type of test (distribution; z, t, etc.) Questions to ask: a. Can we assume a normally distributed sampling distribution? In other words, do we have 30+ participants OR a normally distributed population? If yes, then continue. If no, do not continue, the test cannot be performed. b. Do we know the population standard deviation? If yes, then use o to estimate og and perform a Z-test 08 = 1500 If no, then use s to estimate sx and perform a t-test Sx = Find critical value & state decision rule Critical Value Questions to ask: a. Is this a 1-tailed or a 2-tailed test? b. If it is a t-test what are the degrees of freedom (DF)? If this is a Z-test, find the z-value(s) that correspond to alpha (e.g. 1.96, 1.64) and that is your critical value. If this is a t-test, use alpha, the number of tails and the degrees of freedom to look up the critical value in a t-table. Decision Rule In words: If If numbers: If Calculate test Apply decision rule Since, the null hypothesis. observed is larger than reject the null hypothesis χ-μ σx or sx critical reject the null hypothesis = -(i.e.observed value) (i.e. >,<)————(critical value), (ie.DO or DO NOT) reject

John works as a "sanitation engineer" for a zoo that has only 10 elephants and 8 zebras in the whole zoo (a budgetary problem). Every day he goes to work he feels like he is shoveling a great deal of waste and he wants to know if the amount of waste that he disposes of on average is different than the normal amount elephant/zebra zoos dispose of. On any given day 1500 pounds of waste, with a standard deviation of 500 pounds, are removed from these types of facilities across the country, however John shovels 1700 pounds of waste a day. Is John shoveling significantly more crap than the average facility? State Null Hypothesis ho:μ 1500 Alternative Hypothesis h₁:μ Decide on a (usually .05) a = Decide on type of test (distribution; z, t, etc.) Questions to ask: a. Can we assume a normally distributed sampling distribution? In other words, do we have 30+ participants OR a normally distributed population? If yes, then continue. If no, do not continue, the test cannot be performed. b. Do we know the population standard deviation? If yes, then use o to estimate og and perform a Z-test 08 = 1500 If no, then use s to estimate sx and perform a t-test Sx = Find critical value & state decision rule Critical Value Questions to ask: a. Is this a 1-tailed or a 2-tailed test? b. If it is a t-test what are the degrees of freedom (DF)? If this is a Z-test, find the z-value(s) that correspond to alpha (e.g. 1.96, 1.64) and that is your critical value. If this is a t-test, use alpha, the number of tails and the degrees of freedom to look up the critical value in a t-table. Decision Rule In words: If If numbers: If Calculate test Apply decision rule Since, the null hypothesis. observed is larger than reject the null hypothesis χ-μ σx or sx critical reject the null hypothesis = -(i.e.observed value) (i.e. >,<)————(critical value), (ie.DO or DO NOT) reject

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 13PPS
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John works as a "sanitation engineer" for a zoo that has only 10 elephants and 8 zebras in the whole zoo (a budgetary problem). Every day he goes to work he feels like he is shoveling a great deal of waste and he wants to know if the amount of waste that he disposes of on average is different than the normal amount elephant/zebra zoos dispose of. On any given day 1500 pounds of waste, with a standard deviation of 500 pounds, are removed from these types of facilities across the country, however John shovels 1700 pounds of waste a day. Is John shoveling significantly more crap than the average facility? State Null Hypothesis ho:μ____1500 Alternative Hypothesis h₁: μ Decide on a (usually .05) a = Decide on type of test (distribution; z, t, etc.) Questions to ask: a. Can we assume a normally distributed sampling distribution? In other words, do we have 30+ participants OR a normally distributed population? If yes, then continue. If no, do not continue, the test cannot be performed. b. Do we know the population standard deviation? If yes, then use o to estimate ox and perform a Z-test 0x = 08 1500 If no, then use s to estimate sx and perform a t-test Sx S8 = Find critical value & state decision rule Critical Value Questions to ask: a. Is this a 1-tailed or a 2-tailed test? b. If it is a t-test what are the degrees of freedom (DF)? If this is a Z-test, find the z-value(s) that correspond to alpha (e.g. 1.96, 1.64) and that is your critical value. If this is a t-test, use alpha, the number of tails and the degrees of freedom to look up the critical value in a t-table. Decision Rule In words: If If numbers: If Calculate test Apply decision rule Since, the null hypothesis. observed is larger than (i.e.observed value) reject the null hypothesis X - μ σx or sx critical reject the null hypothesis -(i.e. >,<) _(critical value), (i.e.DO or DO NOT) reject
Transcribed Image Text:John works as a "sanitation engineer" for a zoo that has only 10 elephants and 8 zebras in the whole zoo (a budgetary problem). Every day he goes to work he feels like he is shoveling a great deal of waste and he wants to know if the amount of waste that he disposes of on average is different than the normal amount elephant/zebra zoos dispose of. On any given day 1500 pounds of waste, with a standard deviation of 500 pounds, are removed from these types of facilities across the country, however John shovels 1700 pounds of waste a day. Is John shoveling significantly more crap than the average facility? State Null Hypothesis ho:μ____1500 Alternative Hypothesis h₁: μ Decide on a (usually .05) a = Decide on type of test (distribution; z, t, etc.) Questions to ask: a. Can we assume a normally distributed sampling distribution? In other words, do we have 30+ participants OR a normally distributed population? If yes, then continue. If no, do not continue, the test cannot be performed. b. Do we know the population standard deviation? If yes, then use o to estimate ox and perform a Z-test 0x = 08 1500 If no, then use s to estimate sx and perform a t-test Sx S8 = Find critical value & state decision rule Critical Value Questions to ask: a. Is this a 1-tailed or a 2-tailed test? b. If it is a t-test what are the degrees of freedom (DF)? If this is a Z-test, find the z-value(s) that correspond to alpha (e.g. 1.96, 1.64) and that is your critical value. If this is a t-test, use alpha, the number of tails and the degrees of freedom to look up the critical value in a t-table. Decision Rule In words: If If numbers: If Calculate test Apply decision rule Since, the null hypothesis. observed is larger than (i.e.observed value) reject the null hypothesis X - μ σx or sx critical reject the null hypothesis -(i.e. >,<) _(critical value), (i.e.DO or DO NOT) reject
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