Last years Class Example was 5 Brown eyes, 15 Blue eyes, 8 green hazel eyes. Did that AP Stats class fit the given model for eye color of Americans, 68.4 % Brown, 16.6% Blue and 15% green/ other?
Ho: The eye color of last years AP Stats class fits the given model for eye color of Americans Ha: The eye color of last years AP Stats class does not fit the given model for eye color of Americans
Category Observed Expected # Expected brown 5 19 67.857% blue 15 5 17.857% green eyes 8 4 14.286%
The chi squared equals 36.951 with 2 degrees of freedom. Because The two-tailed P value is less than 0.0001 and this difference is very significant we are going to reject H0 at the 0.05 significance level. The sample data imply that last years AP Stats class does not fit the given model for eye color of Americans.
population: Americans sample: one AP Class of 28 students test statistic: Chi Squared Goodness of Fit Test
Does the class fit the nation's model for eye colors? Ho: Eye color of class matches proportions for nation. Ha: The class differs in proportions from nation.
conditions: all observed categories are 1 count or greater (5>1 15>1 8>1) this is indeed categorical data at least 20% of categories have counts of 5 or greater (5=5 15>5 8>5) This is NOT an SRS for the nation. We will remember this, but treat observation as an SRS.
X^2=63.44 df=2 upper tail p value= 0.00000000...16
conclusion: The very low p value leads me to believe that the proportions of eye color in that AP class differs from the national proportions of Americans. Reject the null.
Sample of 28 students from Mrs. Lebzelter's AP Stats class BHS; Chi square test, Goodness of Fit.
Ho: The eye color of last year's model matches the model for American's eye color. Ha: The eye color of last year's model does not match the model for American's eye color.
Observed: Brown - 5 ; Blue - 15 ; Green - 8 Expected: Brown - 19.2 ; Blue - 4.6 ; Green - 4.2
Conditions: all samples are > 1 ; more than 20% of the samples are greater than 5 ; categorical (yes) ; not a simple random sample, but for this example, we will assume it is.
(5-19.2)^2/19.2 + (15 - 4.6)^2/4.6 + (8-4.2)^2/4.2 = 37.45 = x^2 df = 3 - 1 = 2 p value = < .0005 (estimate from book)
Conclusion: This very low p-value corresponds with a highly unlikely chance that the eye color models from AP stats are the same as the national model. With this, the null hypothesis is not accepted.
Population: US citizens Sample: AP stats class Class Size: 28 Chi Square, Goodness of Fit
Ho:The eye color of Ms. Lebzelters previous AP stats class will match the model of all US Citizens. Ha: The eye color of Ms. Lebzelters previous AP stats class will not match the model of all US Citizens.
Observed: 5 Brown, 15 Blue, 8 Green Expected: 19.2 Brown, 4.6 Blue, 4.2 Green
Conditions: This is categorical data, all samples are >1, random sample (assumption)
Conclusion: This p-value is very low which means that the chance the eye color from the AP stats class relates to the eye color of the nation is highly unlikely. Therefore I will reject the null and accept the alternative.
Sample: Mrs. Lebzelters AP statistics class Class Size: 28 Tests: Goodness of Fit, Chi Square Test
Ho:The eye color of last years AP statistics class will match the model for all of the United States citizens eye color. Ha: The eye color of last years AP statistics class will not match the model for all of the United States citizens eye color
Observed: 5 Brown 15 Blue 8 Green
Expected: 19.2 Brown 4.6 Blue 4.2 Green
Conditions: All samples are >1, more than 20% of the samples are greater than 5, this is categorical data, SRS
Conclusion: We do not accept the null hypothesis because the p- value is very low, this means that there is a highly unlikely chance that the eye color models from last years AP statistics class are the same as the United States citizens.
Sample: Ms. Lebzelter's AP Statistics class Population: U.S citizens Class size: 28 Tests: Goodness of fit, Chi square
Ho: The color of Ms. Lebzelter's previous AP Statistics class will match the model of U.S citizens. Ha: The eye color of Ms. Lebzelter's previous AP Statistics class will not match the model for all U.S citizens eye color.
Observed: 5 Brown 15 Blue 8 Green
Expected: 19.2 Brown 4.6 Blue 4.2 Green
Conditions All observed categories are >1 More than 20% of samples are >5 Categorical (yes)
Conclusion: The null hypothesis is not accepted because the p value is low, meaning that there is an unlikely chance that the eye color models from last years AP Statistics class is the same as the U.S citizens.
Sample: Mrs. Lebzelter's previous AP Statistics class Population: United States citizens Class Size/Sample size: 28 students Test: Chi Square GOF
Ho: The eye color of Mrs. Lebzelter's previous AP stats class will match the model for U.S. Citizens eye color. Ha: The eye color of Mrs. Lebzelter's previous AP stats class will not match the model for U.S. Citizens eye color.
Conclusion: Fail to accept the null because the p-value is very low. This means there is a very unlikely chance that the eye colors from last years AP Stats class will match those of the national model.
-The sample is Mrs. Lebzelters AP statistics class last year, class size of 28 students -Tests that will be used are Goodness of Fit and Chi Square Test -Null hypothesis, Ho: The eye color proportions of Mrs. Lebzelter's AP Statistics class last year will match the model for eye color proportions of all united states citizens. -Alternative hypothesis, Ha: The eye color proportions of Mrs. Lebzelter's AP Statistics class last year will match the model for eye color proportions of all united states citizens.
Brown Blue Green
Observed Proportion .179 .536 .286 Observed Number 5 15 8
Expected Proportion .684 .166 .15 Expected Number 19.2 4.6 4.2
Conditions we are checking: all samples are >1, more than 20% of the samples are greater than 5, this is categorical data, SRS (assumed)
Sample: Ms. Lebzelter's AP Statistics class Population: US citizens Class size: 28 Tests: Chi square GOF test
Ho: The color of Ms. Lebzelter's previous AP Statistics class is the same as the distribution of eye color in US citizens. Ha: The eye color of Ms. Lebzelter's previous AP Statistics class is not the same as the distribution for all US citizens' eye color.
Observed: 5 Brown 15 Blue 8 Green
Expected: 19.2 Brown 4.6 Blue 4.2 Green
Conditions All observed categories are >1 More than 20% of samples are >5 Categorical, SRS
Conclusion: We fail to accept the null because the p value is too low, meaning that there is an unlikely chance that the eye color models from last years AP Statistics class is the same as that of U.S citizens.
Ho: The color of theAP Stats class will match the model of U.S citizens. Ha: The eye color of the AP Stats class will not match the model for all U.S citizens eye color.
Observed: 5 Brown 15 Blue 8 Green
Expected: 19.2 Brown 4.6 Blue 4.2 Green
Conditions All observed categories are greater than 1 More than 20% of samples are greater than 5 Df=2
Conclusion: I failed to except the null hypothesis because there was a very low probability that the eye color of the AP Stats class matched the U.S proportion.
Ho: The eye color of last years AP Stats class fits the given model for eye color of Americans
ReplyDeleteHa: The eye color of last years AP Stats class does not fit the given model for eye color of Americans
Category Observed Expected # Expected
brown 5 19 67.857%
blue 15 5 17.857%
green eyes 8 4 14.286%
The chi squared equals 36.951 with 2 degrees of freedom. Because The two-tailed P value is less than 0.0001 and this difference is very significant we are going to reject H0 at the 0.05 significance level. The sample data imply that last years AP Stats class does not fit the given model for eye color of Americans.
population: Americans
ReplyDeletesample: one AP Class of 28 students
test statistic: Chi Squared
Goodness of Fit Test
Does the class fit the nation's model for eye colors?
Ho: Eye color of class matches proportions for nation.
Ha: The class differs in proportions from nation.
conditions:
all observed categories are 1 count or greater (5>1 15>1 8>1)
this is indeed categorical data
at least 20% of categories have counts of 5 or greater (5=5 15>5 8>5)
This is NOT an SRS for the nation. We will remember this, but treat observation as an SRS.
X^2=63.44
df=2
upper tail p value= 0.00000000...16
conclusion: The very low p value leads me to believe that the proportions of eye color in that AP class differs from the national proportions of Americans. Reject the null.
Sample of 28 students from Mrs. Lebzelter's AP Stats class BHS; Chi square test, Goodness of Fit.
ReplyDeleteHo: The eye color of last year's model matches the model for American's eye color.
Ha: The eye color of last year's model does not match the model for American's eye color.
Observed: Brown - 5 ; Blue - 15 ; Green - 8
Expected: Brown - 19.2 ; Blue - 4.6 ; Green - 4.2
Conditions: all samples are > 1 ; more than 20% of the samples are greater than 5 ; categorical (yes) ; not a simple random sample, but for this example, we will assume it is.
(5-19.2)^2/19.2 + (15 - 4.6)^2/4.6 + (8-4.2)^2/4.2 = 37.45 = x^2
df = 3 - 1 = 2
p value = < .0005 (estimate from book)
Conclusion: This very low p-value corresponds with a highly unlikely chance that the eye color models from AP stats are the same as the national model. With this, the null hypothesis is not accepted.
Population: US citizens
ReplyDeleteSample: AP stats class
Class Size: 28
Chi Square, Goodness of Fit
Ho:The eye color of Ms. Lebzelters previous AP stats class will match the model of all US Citizens.
Ha: The eye color of Ms. Lebzelters previous AP stats class will not match the model of all US Citizens.
Observed: 5 Brown, 15 Blue, 8 Green Expected: 19.2 Brown, 4.6 Blue, 4.2 Green
Conditions: This is categorical data, all samples are >1, random sample (assumption)
(5-19.2)^/19.2+(15-4.6)^2/4.6+(8-4.2)^2/4.2
x^2=37.45
df=2
p=>.0001
Conclusion: This p-value is very low which means that the chance the eye color from the AP stats class relates to the eye color of the nation is highly unlikely. Therefore I will reject the null and accept the alternative.
Sample: Mrs. Lebzelters AP statistics class
ReplyDeleteClass Size: 28
Tests: Goodness of Fit, Chi Square Test
Ho:The eye color of last years AP statistics class will match the model for all of the United States citizens eye color.
Ha: The eye color of last years AP statistics class will not match the model for all of the United States citizens eye color
Observed: 5 Brown
15 Blue
8 Green
Expected: 19.2 Brown
4.6 Blue
4.2 Green
Conditions: All samples are >1, more than 20% of the samples are greater than 5, this is categorical data, SRS
(5-19.2)^2/19.2+(15-4.6)^2/4.6+(8-4.2)^2/4.2
x^2=37.45
df=3-1 = 2
p=>.0001
Conclusion: We do not accept the null hypothesis because the p- value is very low, this means that there is a highly unlikely chance that the eye color models from last years AP statistics class are the same as the United States citizens.
Sample: Ms. Lebzelter's AP Statistics class
ReplyDeletePopulation: U.S citizens
Class size: 28
Tests: Goodness of fit, Chi square
Ho: The color of Ms. Lebzelter's previous AP Statistics class will match the model of U.S citizens.
Ha: The eye color of Ms. Lebzelter's previous AP Statistics class will not match the model for all U.S citizens eye color.
Observed:
5 Brown
15 Blue
8 Green
Expected:
19.2 Brown
4.6 Blue
4.2 Green
Conditions
All observed categories are >1
More than 20% of samples are >5
Categorical (yes)
(5-19.2)^/19.2+(15-4.6)^2/4.6+(8-4.2)^2/4.2
x^2=37.45
df=2
p=>.0001
Conclusion:
The null hypothesis is not accepted because the p value is low, meaning that there is an unlikely chance that the eye color models from last years AP Statistics class is the same as the U.S citizens.
Sample: Mrs. Lebzelter's previous AP Statistics class
ReplyDeletePopulation: United States citizens
Class Size/Sample size: 28 students
Test: Chi Square GOF
Ho: The eye color of Mrs. Lebzelter's previous AP stats class will match the model for U.S. Citizens eye color.
Ha: The eye color of Mrs. Lebzelter's previous AP stats class will not match the model for U.S. Citizens eye color.
Observed: Brown=5 Blue=15 Green/Other=8
Expected: Brown=19.2 Blue=4.6 Green/Other=4.2
Conditions: SRS (assume), categorical data, all observed categories are >1, and more than 20% of samples are >5
Test:
X^2= (5-19.2)^2/19.2 + (15 - 4.6)^2/4.6 + (8-4.2)^2/4.2 = 37.45
df= 3-1 = 2
p= >0.0001
Conclusion: Fail to accept the null because the p-value is very low. This means there is a very unlikely chance that the eye colors from last years AP Stats class will match those of the national model.
-The sample is Mrs. Lebzelters AP statistics class last year, class size of 28 students
ReplyDelete-Tests that will be used are Goodness of Fit and Chi Square Test
-Null hypothesis, Ho: The eye color proportions of Mrs. Lebzelter's AP Statistics class last year will match the model for eye color proportions of all united states citizens.
-Alternative hypothesis, Ha: The eye color proportions of Mrs. Lebzelter's AP Statistics class last year will match the model for eye color proportions of all united states citizens.
Brown Blue Green
Observed Proportion .179 .536 .286
Observed Number 5 15 8
Expected Proportion .684 .166 .15
Expected Number 19.2 4.6 4.2
Conditions we are checking: all samples are >1, more than 20% of the samples are greater than 5, this is categorical data, SRS (assumed)
Chai Squared Test:
X^2= (5-19.2)^2/19.2+(15-4.6)^2/4.6+(8-4.2)^2/4.2
X^2=37.45
df=3-1 = 2
p=>.0001
Conclusion:
-Fail to accept null
-Very small p value
-Highly unlikely chance that both models are the same
-Accept alternative
Sample: Ms. Lebzelter's AP Statistics class
ReplyDeletePopulation: US citizens
Class size: 28
Tests: Chi square GOF test
Ho: The color of Ms. Lebzelter's previous AP Statistics class is the same as the distribution of eye color in US citizens.
Ha: The eye color of Ms. Lebzelter's previous AP Statistics class is not the same as the distribution for all US citizens' eye color.
Observed:
5 Brown
15 Blue
8 Green
Expected:
19.2 Brown
4.6 Blue
4.2 Green
Conditions
All observed categories are >1
More than 20% of samples are >5
Categorical, SRS
(5-19.2)^/19.2+(15-4.6)^2/4.6+(8-4.2)^2/4.2
x^2=37.45
df=2
p=>.0001
Conclusion:
We fail to accept the null because the p value is too low, meaning that there is an unlikely chance that the eye color models from last years AP Statistics class is the same as that of U.S citizens.
Chi Square GOF Test
ReplyDeleteHo: The color of theAP Stats class will match the model of U.S citizens.
Ha: The eye color of the AP Stats class will not match the model for all U.S citizens eye color.
Observed:
5 Brown 15 Blue 8 Green
Expected:
19.2 Brown 4.6 Blue 4.2 Green
Conditions
All observed categories are greater than 1
More than 20% of samples are greater than 5
Df=2
((5-19.2)^2/19.2)+((15-4.6)^2/4.6)+((8-4.2)^2/4.2)
x^2=37.45
p=>.0001
Conclusion:
I failed to except the null hypothesis because there was a very low probability that the eye color of the AP Stats class matched the U.S proportion.