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An experiment is performed using 1000 trials to test a new scientific model. There are 10...

An experiment is performed using 1000 trials to test a new scientific model. There are 10 different categories of outcomes. When testing the claim that the observed outcomes agree with the expected frequencies, a test statistic is found to be χ2 = 8.185. Use a 0.05 significance level to test the claim that the actual outcomes agree with the expected frequencies. State the conclusion.

1.

Fail to reject the null hypothesis; there is sufficient evidence to warrant rejection of the claim that the observed outcomes agree with the expected frequencies.
2.

Reject the null hypothesis; there is not sufficient evidence to warrant rejection of the claim that the observed outcomes agree with the expected frequencies.
3.

Reject the null hypothesis; there is sufficient evidence to warrant rejection of the claim that the observed outcomes agree with the expected frequencies.
4.

Fail to reject the null hypothesis; there is not sufficient evidence to warrant rejection of the claim that the observed outcomes agree with the expected frequencies.
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Answer #1

Here, degrees of freedom = 10 - 1 = 9
test statistic, chi-square = 8.185

Now, lets find the p-value
p-value = 0.5156

As p-value > 0.05, fail to reject H0
there is not sufficient evidence to warrant rejection of the claim that the observed outcomes agree with the expected frequencies.

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