Respuesta :
Answer:
[tex]p_v= P(\chi^2_{9}>11.517)=0.2419[/tex]
And on this case if we see the significance level given [tex]\alpha=0.1[/tex] we see that [tex]p_v>alpha[/tex] so we fail to reject the null hypothesis that the observed outcomes agree with the expected frequencies at 10% of significance.
Step-by-step explanation:
A chi-square goodness of fit test determines if a sample data obtained fit to a specified population.
[tex]p_v[/tex] represent the p value for the test
O= obserbed values
E= expected values
The system of hypothesis for this case are:
Null hypothesis: [tex]O_i = E_i[/tex[
Alternative hypothesis: [tex]O_i \neq E_i [/tex]
The statistic to check the hypothesis is given by:
[tex]\chi^2 =\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
On this case after calculate the statistic they got: [tex]\chi^2 = 11.517[/tex]
And in order to calculate the p value we need to find first the degrees of freedom given by:
[tex]df=n-1=10-1=9[/tex], where k represent the number of levels (on this cas we have 10 categories)
And in order to calculate the p value we need to calculate the following probability:
[tex]p_v= P(\chi^2_{9}>11.517)=0.2419[/tex]
And on this case if we see the significance level given [tex]\alpha=0.1[/tex] we see that [tex]p_v>alpha[/tex] so we fail to reject the null hypothesis that the observed outcomes agree with the expected frequencies at 10% of significance.
