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Chapter 9: Q R9.6 (page 615)
Flu vaccine Refer to Exercise. Of the adults who were given the vaccine, got the flu. Do these data provide convincing evidence to support the company’s claim?
There is not sufficient evidence to support the claim.
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Potato chips A company that makes potato chips requires each shipment of
potatoes to meet certain quality standards. If the company finds convincing evidence that more than of the potatoes in the shipment have “blemishes,” the truck will be sent back to the supplier to get another load of potatoes. Otherwise, the entire truckload will be used to make potato chips. To make the decision, a supervisor will inspect a random sample of potatoes from the shipment. He will then perform a test of versus , where p is the true proportion of potatoes with blemishes in a given truckload. The power of the test to detect that , based on a random sample of potatoes and significance level , is Interpret this value.
1 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 must sell it to more than of their customers. You contact a random sample of customers and find that would be willing to pay for the upgrade.
a. Do the sample data give convincing 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. Suppose that 30% of the company’s customers would be willing to pay for the upgrade. The power of the test to detect this fact is Interpret this value.
Tests and confidence intervals The value for a two-sided test of the null hypothesis is
a. Does the confidence interval for μ include ? Why or why not?
b. Does the confidence interval for μ include ? Why or why not?
You are testing against based on an SRS of
observations from a Normal population. The t statistic is
The value
a. falls between 0.01 and 0.02.
b. falls between 0.02 and 0.04.
c. falls between 0.04 and 0.05.
d. falls between 0.05 and 0.25.
e. is greater than 0.25.
Water! A blogger claims that U.S. adults drink an average of five ounce glasses (that’s ounces) of water per day. Researchers wonder if this claim is true, so they ask a random sample of U.S. adults about their daily water intake. A graph of the data shows a roughly symmetric shape with no outliers.
a. State an appropriate pair of hypotheses for a significance test in this setting. Be sure to define the parameter of interest.
b. Check conditions for performing the test in part (a).
c. The confidence interval for the mean daily water intake is to ounces. Based on this interval, what conclusion would you make for a test of the hypotheses in part (a) at the significance level?
d. Do we have convincing evidence that the amount of water U.S. children drink per day differs from ounces? Justify your answer.
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