A new medicine is said to help improve sleep. Eight subjects are picked at random and given the medicine. The means
hours slept for each person were recorded before starting the medication and after.
The test is for paired or matching samples.
Eight people were chosen at random and given drugs to help them sleep better. The average sleep hours for each person are recorded before and after they get drugs.
Assuming a mean difference in sleeping hours before and after drug administration as
The null and alternative hypotheses are stated as follows:
This shows that this hypothesis test is for matching or paired test.
Use the following information to answer the next five exercises. A doctor wants to know if a blood pressure medication is
effective. Six subjects have their blood pressures recorded. After twelve weeks on the medication, the same six subjects
have their blood pressure recorded again. For this test, only systolic pressure is of concern. Test at the 1% significance level.
What is the p-value?
A study was conducted to investigate how effective a new diet was in lowering cholesterol. Results for the
randomly selected subjects are shown in the table. The differences have a normal distribution. Are the subjects’
cholesterol levels lower on average after the diet? Test at the level.
A new windshield treatment claims to repel water more effectively. Ten windshields are tested by simulating rain without
the new treatment. The same windshields are then treated, and the experiment is run again. A hypothesis test is conducted.
Indicate if the hypothesis test is for
a. independent group means, population standard deviations, and/or variances known
b. independent group means, population standard deviations, and/or variances unknown
c. matched or paired samples
d. single mean
e. two proportions
f. single proportion
Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites.
In words, define the random variable of interest for this test.
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