In the context of hypothesis testing, the proposition we wish to test is stated as the _______ hypothesis

A. experimental

B. alternative

C. null

D. control

never have sent parents to jail simply because their innocence was highly hkely). Hypothesis testing takes a different approach: rather than seeking to prove some premise-that the die has been tampered with, for instance- wpothesis testing derives its power and significance by using statistical infer- ence to accept or reject some proposition with some level of statistical confidence. We reject those propositions that are highly statistically unlikely. The theory or proposition that is being tested is known as the null hypothesis, or H.. We simultaneously propose an alternative hypothesis, or H, which must be accepted if the null hypothesis is rejected. In this case, the null hypothesis would be that the die is fair. The alternative hypothesis is that the die has been manipulated in such a way as to deliver a nonrandom out- come. Thus: Ho: the die is fair. H.: the die is "loaded." Researchers generally determine the level of statistical confidence required to reject a null hypothesis before conducting the analysis. Thus, we may decide ex ante that we will reject the null hypothesis if we observe an out- come that would happen less than 1 time in 100 if the null hypothesis were true. This is called the 99-percent confidence level, since the probability that chance alone can explain the outcome is 0.01 or lower. A less rigorous bench- mark would be the 95-percent confidence level. In this case, we would reject the null hypothesis if we observe an outcome that would happen less than 5 times in 100 if the null hypothesis were true. Our null hypothesis in this case is that the die is fair. In other words, our presumption is that the gambler is not cheating. Yet we might also decide to reject that presumption if we observed a highly unlikely outcome that worked to the gambler's advantage. If we were to choose a 99-percent level of confi- dence, for example, a judge might ask to inspect the die if the gambler rolled a winning combination of numbers that would turn up by chance less than 1 time in 100. Once again, this low probability outcome does not prove that the gambler is cheating; it does seem a reasonable justification for inspecting the die. Indeed, casinos will take a particular interest in blackjack players who win improbably large amounts of money; such casino patrons may be lucky, or they may be counting cards. What are the odds of rolling a 6 ten times in a row-the feat that enabled the gambler to win $10,000 from you in our hypothetical example? The prob- ability of rolling ten consecutive 6s is (1/6)", or just over 1 in 60 million! That's far more improbable than the threshold we set up for rejecting the null