9. Hypothesis Testing for One Sample

Explain the procedure for testing a hypothesis using the P-value Approach. What is the criterion for judging whether to reject the null hypothesis?

Drive-thru Time (See Problem 21 in Section 10.3.) The mean waiting time at the drive-thru of a fast-food restaurant from the time an order is placed to the time the order is received is 84.3 seconds. A manager devises a new drive-thru system that he believes will decrease wait time. He initiates the new system at his restaurant and measures the wait time for 10 randomly selected orders. The wait times are provided below.

a. The goal of the research is to determine if wait times have decreased as a result of the new system. Based on this research objective, state the null and alternative hypotheses.

According to the National Center for Health Statistics, 22.4% of adults are smokers. A random sample of 300 adults is obtained.

b. In a random sample of 300 adults, what is the probability that at least 50 are smokers?

Explain the difference between “accepting” and “not rejecting” a null hypothesis.

Explain the procedure for testing a hypothesis using the Classical Approach. What is the criterion for judging whether to reject the null hypothesis?

"MigrainesAccording to the Centers for Disease Control, 15.2% of American adults experience migraine headaches. Stress is a major contributor to the frequency and intensity of headaches. A massage therapist feels that she has a technique that can reduce the frequency and intensity of migraine headaches.

a. Determine the null and alternative hypotheses that would be used to test the effectiveness of the massage therapist’s techniques.

"

"MigrainesAccording to the Centers for Disease Control, 15.2% of American adults experience migraine headaches. Stress is a major contributor to the frequency and intensity of headaches. A massage therapist feels that she has a technique that can reduce the frequency and intensity of migraine headaches.

b. A sample of 500 American adults who participated in the massage therapist’s program results in data that indicate that the null hypothesis should be rejected. Provide a statement that supports the massage therapist’s program.

"

If the consequences of making a Type I error are severe, would you choose the level of significance, α, to equal 0.01, 0.05, or 0.10? Why?

What happens to the probability of making a Type II error, β, as the level of significance, α, decreases? Why?

When observed results are unlikely under the assumption that the null hypothesis is true, we say the result is _____and we reject the null hypothesis.

True or False: When testing a hypothesis using the Classical Approach, if the sample proportion is too many standard deviations from the proportion stated in the null hypothesis, we reject the null hypothesis.

Explain what “statistical significance” means.

"[DATA] Height versus Head Circumference [See Problem 13 in Section 12.3] A pediatrician wants to determine the relation that may exist between a child’s height and head circumference. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the following data:

b. Suppose the researcher wanted to determine if there is a positive association between height and head circumference. What would be the null and alternative hypotheses?"