Are the following statements and valid null and alternative hypotheses

H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

State the null and alternative hypotheses. We want to test whether the mean GPA of students in American colleges is different from 2. The null and alternative hypotheses are:. We want to test whether the mean height of eighth graders is 66 inches. We want to test if college students take less than five years to graduate from college, on the average. We want to test if it takes fewer than 45 minutes to teach a lesson plan. In an issue of U. 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. Test if the percentage of U. If you were conducting a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population, what would the null and alternative hypotheses be?

Some of the following statements refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, H 0 , and the alternative hypothesis. Researchers surveyed a group of randomly selected teen girls living in Massachusetts between 12 and 15 years old. After four years the girls were surveyed again. Sixty-three said they smoked to stay thin.

Is there good evidence that more than thirty percent of the teen girls smoke to stay thin? The alternative hypothesis is:. She surveys 84 of her students and finds that 11 attended the midnight showing. An appropriate alternative hypothesis is:. Previously, an organization reported that teenagers spent 4.

The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4. Conduct a hypothesis test. The null and alternative hypotheses are:. Data from the National Institute of Mental Health. Skip to content Hypothesis Testing with One Sample. Try It. Collaborative Exercise. Chapter Review In a hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim.

In a hypothesis test, we: Evaluate the null hypothesis , typically denoted with H 0. The null is not rejected unless the hypothesis test shows otherwise.

If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis. Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties. Formula Review H 0 and H a are contradictory.

The random variable is the mean Internet speed in Megabits per second. The random variable is the mean number of children an American family has. Homework Some of the following statements refer to the null hypothesis, some to the alternate hypothesis. The mean number of years Americans work before retiring is If the null hypothesis is not rejected, then we do not accept the alternative hypothesis.

If we are studying a new treatment, then the alternative hypothesis is that our treatment does, in fact, change our subjects in a meaningful and measurable way.

The following set of negations may help when you are forming your null and alternative hypotheses. Most technical papers rely on just the first formulation, even though you may see some of the others in a statistics textbook. Actively scan device characteristics for identification.

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