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Chapter 9: Q.107 (page 593)
Normal body temperature (8.3) Check that the conditions are met for performing inference about the mean body temperature in the population of interest.
All conditions have been satisfied.
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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)?
Healthy bones The recommended daily allowance (RDA) of calcium for women between the ages of and years is milligrams (mg). Researchers who were involved in a large-scale study of women鈥檚 bone health suspected that their participants had significantly lower calcium intakes than the RDA. To test this suspicion, the researchers measured the daily calcium intake of a random sample of women from the study who fell in the desired age range. The Minitab output below displays descriptive statistics for these data, along with the results of a significance test.
(a) Determine whether there are any outliers. Show your work.
(b) Interpret the P-value in context.
(c) Do these data give convincing evidence to support the researchers鈥� suspicion? Carry out a test pg to help you answer this question.
You are testing against based on an SRS of observations from a Normal population. What values of the statistic are statistically significant at thelevel?
(a)
(b)
(c)
(d)
(c)
Describe a Type I error in this setting.
A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay for the upgrade. For the upgrade to be profitable, the company needs to sell it to more than of their customers. You contact a random sample of customers and find that 16 would be willing to pay for the upgrade.
(a) Do the sample data give good evidence that more than of the company鈥檚 customers are willing to purchase the upgrade? Carry out an appropriate test at the significance level.
(b) Which would be a more serious mistake in this setting鈥攁 Type I error or a Type II error? Justify your answer.
(c) Other than increasing the sample size, describe one way to increase the power of the test in (a).
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