Answer:
There has been no change in the classifications between the last school year and this school year.
Step-by-step explanation:
A Chi-square test for goodness of fit will be used in this case.
The hypothesis can be defined as:
H₀: The observed frequencies are same as the expected frequencies.
Hₐ: The observed frequencies are not same as the expected frequencies.
The test statistic is given as follows:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]
The expected values are computed using the formula:
[tex]E_{i}=p_{i}\times N[/tex]
Here, N = 300
Use Excel to compute the values.
The test statistic value is:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}=1.662[/tex]
The test statistic value is, 1.662.
The degrees of freedom of the test is:
n - 1 = 4 - 1 = 3
The significance level is, α = 0.05.
Compute the p-value of the test as follows:
p-value = 0.6454
*Use a Chi-square table.
p-value = 0.6454 > α = 0.05.
So, the null hypothesis will not be rejected at 5% significance level.
Thus, concluding that there has been no change in the classifications between the last school year and this school year.
