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Chapter 9: Q.23 (page 548)
You read that a statistical test at significance level=0.05 has power 0.78. What are the probabilities of Type I and Type II errors for this test?
The probabilities are Type I = and Type II error =
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Is it significant? For students without special preparation, SAT Math scores in recent years have varied Normally with mean . One hundred students go through a rigorous training program designed to raise their SAT Math scores by improving their mathematics skills. Use your calculator to carry out a test of
in each of the following situations.
(a) The students' scores have mean and standard deviation . Is this result significant at thelevel?
(b) 'The students' scores have mean and standard deviation . Is this result significant at the level?
(c) When looked at together, what is the intended lesson of (a) and (b)?
The reason we use procedures instead of procedures when carrying out a test about a population mean is that
(a) can be used only for large samples.
(b)requires that you know the population standard deviation .
(c) requires you to regard your data as an SRS from the population.
(d) applies only if the population distribution is perfectly Normal.
(e) can be used only for confidence intervals.
A government report says that the average amount of money spent per U.S. household per week on food is about . A random sample of households in a small city is selected, and their weekly spending on food is recorded. The Minitab output below shows the results of requesting a confidence interval for the population mean M. An examination of the data reveals no outliers.
(a) Explain why the Normal condition is met in this case.
(b) Can you conclude that the mean weekly spending on food in this city differs from the national figure of? Give appropriate evidence to support your answer.
Are TV commercials louder than their surrounding programs? To find out, researchers collected data on randomly selected commercials in a given week. With the television鈥檚 volume at a fixed setting, they measured the maximum loudness of each commercial and the maximum loudness in the first seconds of regular programming that followed. Assuming conditions for inference are met, the most appropriate method for answering the question of interest is
(a) a one-proportion z test.
(b) a one-proportion z interval.
(c) a paired t test.
What is significance good for? Which of the following questions does a significance test answer? Justify your answer.
(a) Is the sample or experiment properly designed?
(b) Is the observed effect due to chance?
(c) Is the observed effect important?
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