6-3 and 6-4 Notes
6-3 Test of Hypothesis about a Population Mean: Normal (z) Statistic
Example 6.3.1.
The effect of drugs and alcohol on the nervous system has been the subject of considerable research. Suppose a research neurologist is testing the effect of a drug on response time by injecting 100 rats with a unit dose of the drug, subjecting each rat to a neurological stimulus, and recording its response time. The neurologist knows that the mean response time for rats not injected with the drug (the “control” mean) is 1.2 seconds. She wishes to test whether the mean response time for drug-injected rats differs from 1.2 seconds. At = .01, conduct the test of hypothesis.
Solution:
Example 6.3.2.
Teenage drivers will inevitably be tempted to drive faster, even to exceed the speed limit, by their friends. Did you resist such temptations when you first began to drive? To gain insight into this phenomenon, psychologists from the United Kingdom conducted a survey of 258 student drivers and reported the results in the British Journal of Educational Psychology (Vol. 80, 2010). One of the variables in interest was the response to the question “Are you confident that you can resist your friends’ persuasion to drive faster?” Each response was measured on a 7-point scale, from 1 = “definitely no” to 7 = “definitely yes.” The data was collected 5 months after the students had attended a safe-driver presentation. They psychologist reported a sample mean response of 4.98 and a sample standard deviation of 1.62. Suppose it is known that the true mean response of students who do not attend a safe-drier presentation is.
Solution:
6.4: Observed Significance Levels: p-Values
Example 6.4.1
The length of stay (in days) for 100 randomly selected hospital patients, presented in the table below. Suppose we want to test the hypothesis that true mean length of stay (LOS) at the hospital is less than 5 days; that is,
(Mean LOS is 5 days)
(Mean LOS is less than 5 days)
Assuming that, use the data in the table to conduct the test of .
Example 6.4.2
In a test of the hypothesis versus, a sample of n = 100 observations possessed mean and standard deviation s = 4.1. Find the p-value for this test.