A person purchased a slot machine and tested it by playing it 1,137 times. There are 10 different categories of outcomes, including no win, win jackpot, win with three bells, and so on. When testing the claim that the observed outcomes agree with the expected frequencies, the author obtained a test statistic of x2 = 11.517. Use a .10 significance level to test the claim that the actual outcomes agree with the expected frequencies.What is the P-Value?

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 testO= obserbed valuesE= expected valuesThe 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.