In n elections between two candidates the regular vote count came out in favor o

Question

In n elections between two candidates the regular vote count came out in favor of Candidate A. When the absentee ballots were counted, the percent in favor of Candidate B was so high that B came out ahead overall. Someone conducts a statistical text to see how rare such a difference between the two vote counts would be just by chance to calculate the p-value to be .08. A newspaper writes “this shows that there is roughly a 92 percent chance that the difference between the two counts is due to some irregularity other than simply chance alone.” Do you agree with the newspaper’s interpretation of the p-value? Explain briefly?

Explanation / Answer

A p-value is a measure of how much evidence we have against the nullhypothesis. The p-value measures consistency by calculating the probability ofobserving the results from your sample of data or a sample with results moreextreme, assuming the null hypothesis is true. We will reject the null hypothesis,when the p-value is less than the signiFcance level of the test.

Null hypothesis, H0: There is no difference between the vote counts of A and B.

Alternate hypothesis, Ha: There is significant difference between the vote counts of A and B.

If p-value < alpha (0.05), we reject the null hypothesis and conclude that there is significant difference between the two groups.

If p-value > alpha (0.05), we fail to reject the null and conclude that there is no difference between the two groups.

Here, we have p-value = 0.08 which is greater than alpha i.e. 0.05. So, we fail to reject the null and claim that their is no difference between the vote counts of both candidates A and B, and the difference is due to some irregularity other than simply chance alone.

So, the interpretation by the newspaper is correct.

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