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Rama09 [41]
3 years ago
5

A person purchased a slot machine and tested it by playing it 1,137 times. There are 10 different categories of outcomes, includ

ing 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?
Mathematics
1 answer:
ivann1987 [24]3 years ago
6 0

Answer:

p_v= P(\chi^2_{9}>11.517)=0.2419

And on this case if we see the significance level given \alpha=0.1 we see that p_v>alpha 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.

p_v represent the p value for the test

O= obserbed values

E= expected values

The system of hypothesis for this case are:

Null hypothesis: O_i = E_i[/tex[Alternative hypothesis: [tex]O_i \neq E_i

The statistic to check the hypothesis is given by:

\chi^2 =\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}

On this case after calculate the statistic they got: \chi^2 = 11.517

And in order to calculate the p value we need to find first the degrees of freedom given by:

df=n-1=10-1=9, 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:

p_v= P(\chi^2_{9}>11.517)=0.2419

And on this case if we see the significance level given \alpha=0.1 we see that p_v>alpha so we fail to reject the null hypothesis that the observed outcomes agree with the expected frequencies at 10% of significance.

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