Historically, the average temperature for the month of January (31 days) has been 33 °F. A...
Historically, the average temperature for the month of January (31 days) has been 33 °F. A meteorologist claims that our winters are getting harsher because the average temperature this January was only 30 °F. It is assumed that the historic standard deviation of 2.5 °F represents the population standard deviation. a) State the null and alternative hypotheses. (4 pts) b) Is this a right-tailed, left-tailed, or two-tailed test? (2 pts) c) Calculate the test-statistic. (6 pts) d) Find the P-value. (3 pts) e) Make a decision about the null hypothesis at the α = 0.01 significance level. Summarize the results in terms of the problem and alternative. (5 pts) f) Based on your decision in Part (e), what type of error (I or II) have you possibly made? What is its interpretation within the context of this problem?
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Historically, the average temperature for the month of January
(31 days) has been 33 °F. A...
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A new virus has been sweeping across the U.S. Health officials
are interested in the average ages of men and women who end up
infected with the virus. In a random sample of 200 men with the
virus their average age was 60 years old with a standard deviation
15 years. In a random sample of 250 women with the virus their
average age was 64 years old with a standard deviation of 10 years.
Test whether the actual average...
A commercial bakery's ovens are designed to bake cakes at a
temperature of 350.0 °F. The ovens are calibrated so that their
temperatures should be normally distributed with a mean of 350.0 °F
and a standard deviation of 4.4 °F. During a recent inspection, the
bakery's quality control supervisor selected a random sample of 12
ovens and recorded their temperatures. She recorded her summary
statistics in the following table.
test of ?=350.0 vs ?≠350.0the assumed standard
deviation=4.4significance level of ?=0.05test...
It is assumed that the mean weight of a Labrador retriever is 70 pounds. A breeder claims that the average weight of an adult male Labrador retriever is not equal to 70 pounds. A random sample of 45 male Labradors weigh an average of 73.6 pounds with a standard deviation of 15.1 pounds. Test the breeder's claim at a = 0.01. Part a: State the null and alternate hypothesis. Part b: Sketch, label and shade the rejection region. Part c:...
It has long been stated that the mean temperature of humans is 98.6°F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6°F. They measured the temperatures of 42 healthy adults 1 to 4 times daily for 3 days, obtaining 196 measurements. The sample data from those 196 measurements resulted in a sample mean of 98.4°F and a sample standard deviation of 0.9°F. Use the P-value approach to conduct a hypothesis...
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