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{"sheet":"Topics","index":0,"n_rows":6,"n_cols":1,"rows_kept":6,"cut":false,"hidden":false,"merged":[]}
["5 Steps in Hypothesis Testing"]
["P-value method"]
["Critical value method"]
["Sigma Known: use z Distribution"]
["Proportion when 4 Binomial Tests are met: use z Distribtion"]
["Sigma NOT Known: use t Distribution"]

{"sheet":"HT-z-upper","index":1,"n_rows":56,"n_cols":16,"rows_kept":56,"cut":false,"hidden":false,"merged":[]}
[null,null,"Mew = population mean = μ",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Left"]
[null,null,"Sigma = population standard deviation = s",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Right"]
[null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE",null,null,null,null,null,null,null,null,null,null,null,null,"Two Tail"]
[null,null,"Hypothesized Value of Population Mean = μ0 = Assumed Value of Population Mean used for testing procedure"]
[null,null,"sample size = n"]
[null,null,"Sample Mean = Xbar"]
[null,null,"Sample Standard Deviation (for when sigma not known) = s"]
[null,null,"Alpha = a = Risk of rejecting (Original Statement) H0 when it is actually true = Type 1 Error"]
[null,null,"Test Statistic = Used to determine whether to reject H0 and accept Ha = Number of SE above or below hypothesized mean"]
[null,null,"Use z test statistic if Sigma known or can be estimated, or you are significance Testing a Proportion and all 4 binomial tests have been met"]
[null,null,"Use t test statistic if Sigma NOT known or can be estimated"]
[]
[null,null,"A statement from an official report said that Realtors make $85,000 a year (national mean). Researcher thinks that Realtors in the Des Moines area have a mean annual salary of more than 85,000 a year. At alpha = .05, sigma = $12,549, n = 36 and sample mean = $88,595, can we conclude that realtors in the Des Moines area make more than $85,000?"]
[]
[null,null,"Hypothesis Test (Significance Test)"]
[null,null,"Point of view:"]
[null,null,"Considering:"]
[null,null,"Goal:"]
[]
["Sample Salaries",null,"Step 1: List H0 and Ha"]
[98356]
[120491.99999999935]
[119398,null,"Step 2: Select Alpha","Alpha =",null,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[92682,null,null,null,null,"At alpha = 0.05, 5% risk of rejecting H0 even though it was true, if we reject Mew <= $85,000, about 5 out of 100 times we will be incorrect."]
[113284,null,"Step 3: Draw Picture, Collect Data, Calculate Sample Statistics, Calculate Test Statistic"]
[79398,null,"Hypothesized Mean = μ0 ="]
[82503,null,"Sigma = s ="]
[81485,null,"Sample SD = s"]
[84083,null,"Test Statistic To Use:",null,null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\"Because Sigma Known\",IF(D29=\"t\",\"Because Sigma NOT Known\",\"Please Enter a z or t\")))","v":""}]
[76384,null,"sample size = n"]
[86539,null,"Sample Mean = Xbar",null,null," =AVERAGE(values)"]
[69894,null,"Alpha = a ="]
[67810,null,"Type of Test"]
[84219,null,"SE",null,null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\" =Sigma/SQRT(n)\",IF(D29=\"t\",\" =s/SQRT(n)\",IF(OR(D29<>\"z\",D29<>\"t\"),\".\"))))","v":""},null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
[90242,null,{"$f":"\"Test Statistic = \"&IF(D29=\"z\",\"z\",IF(D29=\"t\",\"t\",\"\"))&\" =\"","v":"Test Statistic =  ="},null,null," =(Xbar - μ0)/SE",null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
[104294]
[86642,null,"Step 4: Create p-value Rejection Rule and calculate p-value"]
[85646,null,"Rejection Rule:","p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[73286,null,"p-value One Tail To Right",null,null,null," =1-NORM.S.DIST(z,1)",null,"Probability of getting Test Statistic or higher"]
[65074]
[77829,null,"Step 4: Calculate Critical Value and Critical Value Rejection Rule"]
[106881,null,"Rejection Rule:","Test Statistic >= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[83221,null,"Critical Value One Tail To Right",null,null,null," =NORM.S.INV(1-alpha)",null,"This is the hurdle Point"]
[88483]
[80998]
[84734,null,"Step 5: Write Conclusion"]
[126949]
[64085]
[81469]
[85769]
[98864]
[92132]
[65025]
[101594]
[91250]
[98426]

{"sheet":"HT-z-upper (an)","index":2,"n_rows":56,"n_cols":16,"rows_kept":56,"cut":false,"hidden":false,"merged":[]}
[null,null,"Mew = population mean = μ",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Left"]
[null,null,"Sigma = population standard deviation = s",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Right"]
[null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE",null,null,null,null,null,null,null,null,null,null,null,null,"Two Tail"]
[null,null,"Hypothesized Value of Population Mean = μ0 = Assumed Value of Population Mean used for testing procedure"]
[null,null,"sample size = n"]
[null,null,"Sample Mean = Xbar"]
[null,null,"Sample Standard Deviation (for when sigma not known) = s"]
[null,null,"Alpha = a = Risk of rejecting (Original Statement) H0 when it is actually true = Type 1 Error"]
[null,null,"Test Statistic = Used to determine whether to reject H0 and accept Ha = Number of SE above or below hypothesized mean"]
[null,null,"Use z test statistic if Sigma known or can be estimated, or you are significance Testing a Proportion and all 4 binomial tests have been met"]
[null,null,"Use t test statistic if Sigma NOT known or can be estimated"]
[]
[null,null,"A statement from an official report said that Realtors make $85,000 a year (national mean). Researcher thinks that Realtors in the Des Moines area have a mean annual salary of more than 85,000 a year. At alpha = .05, sigma = $12,549, n = 36 and sample mean = $88,595, can we conclude that realtors in the Des Moines area make more than $85,000?"]
[]
[null,null,"Hypothesis Test (Significance Test)"]
[null,".","Point of view:","Researcher who believes that Des Moines realtors have an annual mean greater than $85,000"]
[null,".","Considering:","Population of Des Moines Realtors"]
[null,".","Goal:","Run Hypothesis test to provide statistical evidence to support the claim that Des Moines"]
[null,{"$f":"IF(B18=\"\",\"\",\".\")","v":"."},null,"Realtors have an annual mean salary of more than $85,000. Mew > 85000 >>> 1 tail right"]
["Sample Salaries",null,"Step 1: List H0 and Ha","H0 : μ "," <=",{"$f":"D26","v":85000}]
[98356,null,null,"Ha : μ "," >",{"$f":"D26","v":85000}]
[120491.99999999935]
[119398,null,"Step 2: Select Alpha","Alpha =",0.05,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[92682,null,null,null,null,"At alpha = 0.05, 5% risk of rejecting H0 even though it was true, if we reject Mew <= $85,000, about 5 out of 100 times we will be incorrect."]
[113284,null,"Step 3: Draw Picture, Collect Data, Calculate Sample Statistics, Calculate Test Statistic"]
[79398,null,"Hypothesized Mean = μ0 =",85000]
[82503,null,"Sigma = s =",12549]
[81485,null,"Sample SD = s","NA"]
[84083,null,"Test Statistic To Use:","z",null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\"Because Sigma Known\",IF(D29=\"t\",\"Because Sigma NOT Known\",\"Please Enter a z or t\")))","v":"Because Sigma Known"}]
[76384,null,"sample size = n",{"$f":"COUNT(A21:A56)","v":36}]
[86539,null,"Sample Mean = Xbar",{"$f":"AVERAGE(A21:A56)","v":88594.999999999971},null," =AVERAGE(values)"]
[69894,null,"Alpha = a =",{"$f":"E23","v":0.05}]
[67810,null,"Type of Test","One Tail To Right"]
[84219,null,"SE",{"$f":"D27/SQRT(D30)","v":2091.5},null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\" =Sigma/SQRT(n)\",IF(D29=\"t\",\" =s/SQRT(n)\",IF(OR(D29<>\"z\",D29<>\"t\"),\".\"))))","v":" =Sigma/SQRT(n)"},null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
[90242,null,{"$f":"\"Test Statistic = \"&IF(D29=\"z\",\"z\",IF(D29=\"t\",\"t\",\"\"))&\" =\"","v":"Test Statistic = z ="},{"$f":"(D31-D26)/D34","v":1.718862060721956},null," =(Xbar - μ0)/SE",null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
[104294]
[86642,null,"Step 4: Create p-value Rejection Rule and calculate p-value"]
[85646,null,"Rejection Rule:","p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[73286,null,"p-value One Tail To Right",{"$f":"1-_xlfn.NORM.S.DIST(D35,1)","v":4.2819745911792384E-2},null,null," =1-NORM.S.DIST(z,1)",null,"Probability of getting Test Statistic or higher"]
[65074]
[77829,null,"Step 4: Calculate Critical Value and Critical Value Rejection Rule"]
[106881,null,"Rejection Rule:","Test Statistic >= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[83221,null,"Critical Value One Tail To Right",{"$f":"_xlfn.NORM.S.INV(1-D32)","v":1.6448536269514715},null,null," =NORM.S.INV(1-alpha)",null,"This is the hurdle Point"]
[88483]
[80998]
[84734,null,"Step 5: Write Conclusion"]
[126949,".","Because the p-value of 0.043 <= alpha of 0.05, we reject H0 and accept Ha."]
[64085,".","Because the test statistic of 1.72 >= critical value of 1.645, we reject H0 and accept Ha."]
[81469,".","The statistical evidence suggests that the mean annual salary for realtors in Des Moines is"]
[85769,{"$f":"IF(B49=\"\",\"\",\".\")","v":"."},"greater than the national mean."]
[98864,".","At an alpha of 0.05, our sample mean of $88,595 provides statistically significant evidence that"]
[92132,{"$f":"IF(B51=\"\",\"\",\".\")","v":"."},"the mean annual salary for realtors in Des Moines is greater than the national mean."]
[65025,".","We do run a 5% risk of a Type 1 Error that we might say that the mean annual salary for"]
[101594,{"$f":"IF(B53=\"\",\"\",\".\")","v":"."},"realtors in Des Moines is greater than $85,00, when it is not greater than $85,000."]
[91250]
[98426]

{"sheet":"HT-z-upper (anxxx)","index":3,"n_rows":56,"n_cols":16,"rows_kept":56,"cut":false,"hidden":true,"merged":[]}
[null,null,"Mew = population mean = μ",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Left"]
[null,null,"Sigma = population standard deviation = s",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Right"]
[null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE",null,null,null,null,null,null,null,null,null,null,null,null,"Two Tail"]
[null,null,"Hypothesized Value of Population Mean = μ0 = Assumed Value of Population Mean used for testing procedure"]
[null,null,"sample size = n"]
[null,null,"Sample Mean = Xbar"]
[null,null,"Sample Standard Deviation (for when sigma not known) = s"]
[null,null,"Alpha = a = Risk of rejecting (Original Statement) H0 when it is actually true = Type 1 Error"]
[null,null,"Test Statistic = Used to determine whether to reject H0 and accept Ha = Number of SE above or below hypothesized mean"]
[null,null,"Use z test statistic if Sigma known or can be estimated, or you are significance Testing a Proportion and all 4 binomial tests have been met"]
[null,null,"Use t test statistic if Sigma NOT known or can be estimated"]
[]
[null,null,"A statement from an official report said that Realtors make $85,000 a year (national mean). Researcher thinks that Realtors in the Des Moines area have a mean annual salary of more than 85,000 a year. At alpha = .05, sigma = $12,549, n = 36 and sample mean = $88,595, can we conclude that realtors in the Des Moines area make more than $85,000?"]
[]
[null,null,"Hypothesis Test (Significance Test)"]
[null,".","Point of view:","Researcher who believes that Des Moines realtors have an annual mean greater than $85,000"]
[null,".","Considering:","Population of Des Moines Realtors"]
[null,".","Goal:","Run Hypothesis test to provide statistical evidence to support the claim that Des Moines"]
[null,{"$f":"IF(B18=\"\",\"\",\".\")","v":"."},null,"Realtors have an annual mean salary of more than $85,000. Mew > 85000 >>> 1 tail right"]
["Sample Salaries",null,"Step 1: List H0 and Ha","H0 : μ"," <=",{"$f":"D26","v":85000}]
[98356,null,null,"Ha : μ"," >",{"$f":"D26","v":85000}]
[120491.99999999935]
[119398,null,"Step 2: Select Alpha","Alpha =",0.05,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[92682,null,null,null,null,"At alpha = 0.05, 5% risk of rejecting H0 even though it was true, if we reject Mew <= $85,000, about 5 out of 100 times we will be incorrect."]
[113284,null,"Step 3: Draw Picture, Collect Data, Calculate Sample Statistics, Calculate Test Statistic"]
[79398,null,"Hypothesized Mean = μ0 =",85000]
[82503,null,"Sigma = s =",12549]
[81485,null,"Sample SD = s","NA"]
[84083,null,"Test Statistic To Use:","z",null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\"Because Sigma Known\",IF(D29=\"t\",\"Because Sigma NOT Known\",\"Please Enter a z or t\")))","v":"Because Sigma Known"}]
[76384,null,"sample size = n",{"$f":"COUNT(A21:A56)","v":36}]
[86539,null,"Sample Mean = Xbar",{"$f":"AVERAGE($A$21:$A$56)","v":88594.999999999971},null," =AVERAGE(values)"]
[69894,null,"Alpha = a =",{"$f":"E23","v":0.05}]
[67810,null,"Type of Test","One Tail To Right"]
[84219,null,"SE",{"$f":"D27/SQRT(D30)","v":2091.5},null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\" =Sigma/SQRT(n)\",IF(D29=\"t\",\" =s/SQRT(n)\",IF(OR(D29<>\"z\",D29<>\"t\"),\".\"))))","v":" =Sigma/SQRT(n)"},null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
[90242,null,{"$f":"\"Test Statistic = \"&IF(D29=\"z\",\"z\",IF(D29=\"t\",\"t\",\"\"))&\" =\"","v":"Test Statistic = z ="},{"$f":"(D31-D26)/D34","v":1.718862060721956},null," =(Xbar - μ0)/SE",null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
[104294]
[86642,null,"Step 4: Create p-value Rejection Rule and calculate p-value"]
[85646,null,"Rejection Rule:","p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[73286,null,"p-value One Tail To Left",{"$f":"1-_xlfn.NORM.S.DIST(D35,1)","v":4.2819745911792384E-2},null,null," =1-NORM.S.DIST(z,1)",null,"Probability of getting Test Statistic or higher"]
[65074]
[77829,null,"Step 4: Calculate Critical Value and Critical Value Rejection Rule"]
[106881,null,"Rejection Rule:","Test Statistic <= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[83221,null,"Critical Value One Tail To Left",{"$f":"_xlfn.NORM.S.INV(1-D32)","v":1.6448536269514715},null,null," =NORM.S.INV(1-alpha)",null,"This is the hurdle Point"]
[88483]
[80998]
[84734,null,"Step 5: Write Conclusion"]
[126949,".","Because the p-value of 0.043 <= alpha of 0.05, we reject H0 and accept Ha."]
[64085,".","Because the test statistic of 1.72 >= critical value of 1.645, we reject H0 and accept Ha."]
[81469,".","The statistical evidence suggests that the mean annual salary for realtors in Des Moines is"]
[85769,{"$f":"IF(B49=\"\",\"\",\".\")","v":"."},"greater than the national mean."]
[98864,".","At an alpha of 0.05, our sample mean of $88,595 provides statistically significant evidence that"]
[92132,{"$f":"IF(B51=\"\",\"\",\".\")","v":"."},"the mean annual salary for realtors in Des Moines is greater than the national mean."]
[65025,".","We do run a 5% risk of a Type 1 Error that we might say that the mean annual salary for"]
[101594,{"$f":"IF(B53=\"\",\"\",\".\")","v":"."},"realtors in Des Moines is greater than $85,00, when it is not greater than $85,000."]
[91250]
[98426]