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Chapter 9: Q.17 (page 547)
Explain in plain language why a significance test that is significant at the 1% level must always be significant at the 5% level. If a test is significant at the 5% level, what can you say about its significance at the 1% level?
It is not known the significance atlevel.
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Radon detectors Radon is a colorless, odorless gas that is naturally released by rocks and soils and may concentrate in tightly closed houses. Because radon is slightly radioactive, there is some concern that it may be a health hazard. Radon detectors are sold to homeowners worried about this risk, but the detectors may be inaccurate. University researchers placed a random sample of detectors in a chamber where they were exposed to picocuries per liter of radon over days. A graph of the radon readings from the detectors shows no strong skewness or outliers. The Minitab output below shows the results of a one-sample t interval. Is there significant evidence at the level that the mean reading differs from the true value ? Give appropriate evidence to support your answer.
Strong chairs? A company that manufactures classroom chairs for high school students claims that the mean breaking strength of the chairs that they make is pounds. One of the chairs collapsed beneath a -pound student last week. You wonder whether the manufacturer is exaggerating the breaking strength of the chairs.
(a) State null and alternative hypotheses in words and symbols.
(b) Describe a Type I error and a Type II error in this situation, and give the consequences of each.
(c) Would you recommend a significance level of, or for this test? Justify your choice.
(d) The power of this test to detect is . Explain what this means to someone who knows little statistics.
(e) Explain two ways that you could increase the power of the test from (d).
- If conditions are met, conduct a significance test about a population proportion.
Haemoglobin is a protein in red blood cells that carries oxygen from the lungs to body tissues. People with less than 12 grams of haemoglobin per deciliter of blood (g/dl) are anaemic. A public health official in Jordan suspects that Jordanian children are at risk of anaemia. He measures a random sample of 50 children.
A confidence interval for a population mean is calculated to be . Assume that the conditions for performing inference are met. What conclusion can we draw for a test of role="math" localid="1650275427722" versus at the level based on the confidence interval?
(a) None. We cannot carry out the test without the original data.
(b) None. We cannot draw a conclusion at the level since this test is connected to the confidence interval.
(c) None. Confidence intervals and significance tests are unrelated procedures.
(d) We would reject at level .
(e) We would fail to reject at level .
A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of one inch could be increased by
(a) using only volunteers from the basketball team in the experiment.
(b) using instead of .
(c) using instead of .
(d) giving the drug to randomly selected students instead of .
(e) using a two-sided test instead of a one-sided test.
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