I'm having a problem with the entire Chi-square thing..
I do have answers to these but I'm not sure how to work them out..
If you could help that would be great! :)
1st part:
A,B,C are schools. Is the choice of math programs followed independently by school? Write the hypotheses.
2nd part:
There is a table with X,Y,Z for rows and S,M,H for rows
XS:28,XM:44,XH:14
YS:20,YM:24,YH:17
ZS:51,ZM:66,ZH:20
show that this table has 4 degrees of freedom and show that expected frequency for YM is 28.78 correct to 2 decimal places.
3rd part:
find the complete Chi-Square statistic..
(I want to know how to get the expected for each cell of the table)
I need this as well......
E for each cell = (row total * column total)/grand total
Degrees of freedom = (number of rows - 1)(number of columns - 1)
To answer your questions about the Chi-square statistical test, let's break down each part:
1st part:
To determine if the choice of math programs is followed independently by school, you need to set up the null and alternative hypotheses. In this case, the null hypothesis (H0) states that the choice of math programs is independent of the school, while the alternative hypothesis (Ha) states that there is a dependence between the choice of math programs and the school.
H0: The choice of math programs is independent of the school
Ha: There is a dependence between the choice of math programs and the school
2nd part:
To calculate the degrees of freedom and the expected frequency, we first need to create an observed frequency table from the given data:
| S M H | Total
----------------------------
X | 28 44 14 | 86
Y | 20 24 17 | 61
Z | 51 66 20 | 137
----------------------------
99 134 51 | 284
The degrees of freedom (df) for a Chi-square test can be calculated using the formula: df = (r-1) * (c-1), where r is the number of rows and c is the number of columns. In our case, r = 3 and c = 3, so df = (3-1) * (3-1) = 4.
To calculate the expected frequency for YM, we can use the formula: Expected Frequency (E) = (row total * column total) / grand total. For YM, the row total is 61, the column total is 134, and the grand total is 284. Substituting these values into the formula, we get: E = (61 * 134) / 284 = 28.783, which rounds to 28.78 when rounded to 2 decimal places.
3rd part:
To find the complete Chi-Square statistic, we need to calculate the expected frequency for each cell in the table and then use the formula:
Chi-square (χ²) = ∑ ((Observed - Expected)² / Expected)
The expected frequency for each cell can be calculated using the formula mentioned earlier: E = (row total * column total) / grand total. Calculate the expected frequency for each cell and substitute it into the formula to calculate the Chi-square statistic. Sum the values across all cells to get the final result.
I hope this explanation helps you understand how to approach the Chi-square test and the calculations involved. Let me know if you have any further questions!