Suppose we perform four goodness of fit tests on seven different data sets, wher

Question

Suppose we perform four goodness of fit tests on seven different data sets, where the test hypothesis is the same for all data sets. Moreover, imagine that the seven p-values we observe are: If we use the 0.05 p-value cutoff as a decision for rejecting/not rejecting the null hypothesis, what is the most likely conclusion we draw from this list of results? We will require more data sets and more p-values to draw a conclusive decision. We reject the null hypothesis that the observed data are consistent with the expected proportions. We really don't like math. We change the p-value threshold from 0.05 so that we can make a more conclusive decision. We do not reject the null hypothesis that the observed data are consistent with the expected proportions.

Explanation / Answer

The goodness of fit test is conducted with the following hypothesis -

Null Hypothesis - The data is consistent with the specified distribution.

Alternate Hypothesis - The data are not consistent with the specified distribution.

We reject the null hypothesis if the p-value of the test is smaller than the significance level of the test.

From the seven p-values obtained, only one has smaller p-value (0.02) than the significance level of 0.05. So, only in one case the null hypothesis will be rejected.

So, in maximum cases we would fail to reject the null hypothesis and conclude that the data is consistent with the distribution.

But it would be better if we change the threshold of the significance level from 0.05 to 0.02. In that case, none of the p-value will be smaller than the significance level and hence we would make a more conclusive decision that the data is consistent with the distribution.

Hence, option (D) is correct.

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