Chi-squared Goodness-of-fit
Χ2 goodness-of-fit test
https://davidwills.us/stat200/chi_sqrGoodness.html
***********************************************************************
Sum of 2 dice probabilities:
sum= 2 3 4 5 6 7 8 9 10 11 12
P= .027777 .055555 .083333 .111111 .1388888 .16666666 .1388888 .111111 .083333 .055555 .027777
n=100 tosses of a die: Copy and paste from the webpage
Ei= 2.7777 5.5555 8.3333 11.1111 13.88888 16.666666 13.88888 11.1111 8.3333 5.5555 2.7777
Do these at 0.95 significance level:
Oi= 2 5 6 17 12 16 13 9 13 7 0
Χ2 statistic=________ Critical value=__________ Reject H0?:______
p_value=________ Reject H0?:______
These 100 rolls are expectable? i.e. within random chance?:_____
Oi= 5 3 7 17 9 11 10 12 14 7 5
Χ2 statistic=________ Critical value=__________ Reject H0?:______
p_value=________ Reject H0?:______
These 100 rolls are expectable? i.e. within random chance?:_____
Oi= 6 3 7 17 9 10 9 12 14 7 6
Χ2 statistic=________ Critical value=__________ Reject H0?:______
p_value=________ Reject H0?:______
These 100 rolls are expectable? i.e. within random chance?:_____
Do this one again but at the 0.99 significance level.
Χ2 statistic=________ Critical value=__________ Reject H0?:______
p_value=________ Reject H0?:______
These 100 rolls are expectable? i.e. within random chance?:_____
***********************************************************************
The day-of-birth data in Nominal Data:
57 52 43 53 57 66 72
n=400 births, assume uniform distribution, so each day equally likely, so each Ei =400/7= 57.14
Do at 0.95 significance level.
Χ2 statistic=________ Critical value=__________ Reject H0?:______
p_value=________ Reject H0?:______
These birth days are expectable? i.e. within random chance?:_____
***********************************************************************
Kentucky Derby. #winners from gate position
Oi= 9 14 11 15 16 7 9 12 5 11 =119
Assume uniform: every E=119/10= 11.9
Χ2 statistic=________ Critical value=__________ Reject H0?:______
p_value=________ Reject H0?:______
These winning gate positions are expectable? i.e. within random chance?:_____
Modified winners (for educational purposes)
Oi= 19 16 15 15 16 7 9 8 5 7 =119
Χ2 statistic=________ Critical value=__________ Reject H0?:______
p_value=________ Reject H0?:______
These winning gate positions are expectable? i.e. within random chance?:_____
Now change the confidence level to 0.99
Χ2 statistic=________ Critical value=__________ Reject H0?:______
p_value=________ Reject H0?:______
These winning gate positions are expectable? i.e. within random chance?:_____
Changing the confidence level changed which calculated values:_______