Hypothesis Testing of Single Mean and Single Proportion: Null and Alternate Hypotheses 1.4 2008/06/06 17:19:18 GMT-5 2008/07/18 10:38:19.219 GMT-5 Barbara Illowsky illowskybarbara@deanza.edu Susan Dean deansusan@deanza.edu Connexions cnx@cnx.org elementary statistics The actual test begins by considering two hypotheses. They are called the null hypothesis and the alternate hypothesis. These hypotheses contain opposing viewpoints. H o : The null hypothesis: It is what is believed or assumed to be true about the population unless it can be shown to be incorrect beyond a reasonable doubt. H a : The alternate hypothesis: It is a claim about the population that is contradictory to Ho and what we conclude when we reject Ho.Ho: No more than 30% of the registered voters in Santa Clara County voted in the primary election. H a : More than 30% of the registered voters in Santa Clara County voted in the primary election. We want to test whether the average grade point average in American colleges is 2.0 (out of 4.0) or not. H a : μ = 2.0 Ho : μ ≠ 2.0 We want to test if college students take less than five years to graduate from college, on the average. Ho: μ ≥ 5 H a : μ 5 In an issue of U. S. News and World Report, an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U. S. students take advanced placement exams and 4.4 % pass. Test if the percentage of U. S. students who take advanced placement exams is more than 6.6%. Ho: p=0.066 H a : p > 0.066 Since the null and alternate hypotheses are contradictory, you must examine evidence to decide which hypothesis the evidence supports. The evidence is in the form of sample data. The sample might support either the null hypothesis or the alternate hypothesis but not both. After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are "reject Ho" if the sample information favors the alternate hypothesis or "do not reject Ho" if the sample information favors the null hypothesis, meaning that there is not enough information to reject the null. Mathematical Symbols Used in Ho and Ha: Ho Ha equal (=) not equal (≠) or greater than (>) or less than () greater than or equal to (≥) less than () less than or equal to (≤) more than (>) Ho always has a symbol with an equal in it. Ha never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test.

Optional Collaborative Classroom Activity Bring to class a newspaper, some news magazines, and some Internet articles . In groups, find articles from which your group can write a null and alternate hypotheses. Discuss your hypotheses with the rest of the class.

Hypothesis A statement about the value of a population parameter. In case of two hypotheses, the statement assumed to be true is called null hypothesis (notation H0 size 12{H rSub { size 8{0} } } {}) and contradictory statement is called alternate hypothesis (notation Ha size 12{H rSub { size 8{a} } } {}).