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Chapter 9: Q. 9.6 (page 509)
Suppose the null hypothesis, , is: a patient is not sick. Which type of error has the greater consequence, Type or Type?
Type one error is the patient is sick which is opposite to the fact.
Type two error is the patient is not sick which is opposite to the fact.
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A particular brand of tires claims that its deluxe tire averages at least miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be . A survey of owners of that tire design is conducted. From the tires surveyed, the mean lifespan was miles with a standard deviation of miles. Using alpha =, is the data highly inconsistent with the claim?
From generation to generation, the mean age when smokers first start to smoke varies. However , the standard deviation pf that age remains constant of around years . A survey of smokers of this generation was done to see if the mean starting age is at least . the sample mean was with a sample standard deviation ofdo the data support the claim at the level?
The National Institute of Mental Health published an article stating that in any one-year period, approximately percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct 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.
a. Is this a test of one mean or proportion?
b. State the null and alternative hypotheses.
c. Is this a right-tailed, left-tailed, or two-tailed test?
d. What symbol represents the random variable for this test?
e. In words, define the random variable for this test.
f. Calculate the following:
i.
ii.role="math" localid="1649760873126"
iii.
g. Calculate role="math" localid="1649760901479" Show the formula set-up.
h. State the distribution to use for the hypothesis test.
i. Find the -value.
j. At a pre-conceived , what is your:
i. Decision:
ii. Reason for the decision:
iii. Conclusion (write out in a complete sentence):
Your friend claims that his mean golf score is 63. You want to show that it is higher than that. What type of test would
you use?
Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is years. A study was then done to see if the meantime has increased in the new century. A random sample of first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was years with a standard deviation of years. Suppose that it is somehow known that the population standard deviation is . If you were conducting a hypothesis test to determine if the mean length of jail time has increased, what would the null and alternative hypotheses be? The distribution of the population is normal.
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