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Chapter 9: Q.2.2 (page 539)
Describe a Type II error in this setting.
Type II error happens in the event that the null hypothesis isn't dismissed regardless of whether it isn't right.
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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’s 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—a 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).
Sampling shoppers A marketing consultant observes consecutive shoppers at a supermarket, recording how much each shopper spends in the store. Explain why it would not be wise to use these data to carry out a significance test about the mean amount spent by all shoppers at this supermarket.
Anemia Hemoglobin is a protein in red blood cells that carries oxygen from the lungs to body tissues. People with fewer than grams of hemoglobin per deciliter of blood are anemic. A public health official in Jordan suspects that Jordanian children are at risk of anemia. He measures a random sample of children. Check the conditions for carrying out a significance test of the official’s suspicion.
How long does it take for a chunk of information to travel from one server to another and back on the Internet? According to the site internettrafficreport.com, a typical response time is milliseconds (about one-fifth of a second). Researchers collected data on response times of a random sample ofservers in Europe. A graph of the data reveals no strong skewness or outliers. The figure below displays Minitab output for a one-sample t interval for the population mean. Is there convincing evidence at the significance level that the site’s claim is incorrect? Use the confidence interval to justify your answer.
The P-value for a two-sided test of the null hypothesis is
(a) Does theconfidence interval forinclude ? Why or why not?
(b) Does the confidence interval forinclude ? Why or why not
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