9.1 Hypothesis testing of single mean and single proportion: null

$H_o$ : 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.

This null and alternative written in notation would look like, $H_o$ : $p$ $=\mathrm{30\%}$ and $H_a$ : $p$ $>\mathrm{30\%}$ The 30% in this hypothesis is the called the hypothesized value and its symbol is $p_o$ , pronounced p-naught. If the data is categorical like it is in this example the general notation of the null hypothesis will be, $H_a$ : $p$ $=p_o$ . There are three possibilities for the alternative hypothesis, $H_a$ : $p$ $\ne p_o$ , or $H_a$ : $p$ $>p_o$ or $H_a$ : $p$ $<p_o$ You will need to read the problem carefully looking for key language to decide which alternative is appropriate for the problem. Hint: To determine the alternative hypothesis look for what the researcher wants to prove true. This is usually found in a question within the story. Also, look for key language. The use of differs, change, or not the same would indicate that the alternative hypothesis is not equal to the hypothesized value. Language such as more than, bigger than, and increasing would tell us that a greater than symbol will be used in the alternative. Likewise, the use of less than, smaller, or decreasing would indicate using a less than symbol in the alternative hypothesis.When working with numerical data the hypothesize value is ${\mu }_o$ , pronounced mu-naught. The general from of the null hypothesis will be, $H_o$ : $\mu ={\mu }_o$ with the three possible alternatives $H_a$ : $\mu \ne {\mu }_o$ or $H_a$ : $\mu >{\mu }_o$ or $H_a$ : $\mu <{\mu }_o$ .

We want to test whether the mean grade point average in American colleges is different from 2.0 (out of 4.0).

$H_o$ : $\mu =2.0$ $H_a$ : $\mu \ne 2.0$

We want to test if college students take less than five years to graduate from college, on the average.

$H_o$ : $\mu =5$ $H_a$ : $\mu < 5$

Walking to class Sam notices many students listening to music with headphones or ear buds. She wonders if more than half the students on campus listen to music while walking on campus.

$H_o$ : $p$ $=\mathrm{50\%}$ $H_a$ : $p$ $>\mathrm{50\%}$