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Chapter 7: Q23E (page 403)
In a test of against, the sample data yielded the test statistic z = 2.17. Find and interpret the p-value for the test.
The p-value is 0.0150, representing the probability of the test statistic being more than 2.17 when the claim is true.
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Minimizing tractor skidding distance. Refer to the Journal of Forest Engineering (July 1999) study of minimizing tractor skidding distances along a new road in a European forest, Exercise 6.37 (p. 350). The skidding distances (in meters) were measured at 20 randomly selected road sites. The data are repeated below. Recall that a logger working on the road claims the mean skidding distance is at least 425 meters. Is there sufficient evidence to refute this claim? Use \(\alpha = .10\)
Consumer Reports evaluated and rated 46 brands of toothpaste. One attribute examined in the study was whether or not a toothpastebrand carries an American Dental Association (ADA) seal verifying effective decay prevention. The data for the 46 brands (coded 1 = ADA seal, 0 = no ADA seal) are listed here.
a. Give the null and alternative hypotheses for testing whether the true proportion of toothpaste brands with the ADA seal verifying effective decay prevention is less than .5.
b. Locate the p-value on the Minitab printout below
c. Make the appropriate conclusion using
A random sample of n observations is selected from a normal population to test the null hypothesis that 碌=10.Specify the rejection region for each of the following combinations of \(Ha,\alpha ,\) and n:
a.\(Ha:\)碌\( \ne 10;\alpha = .05.;n = 14\)
b.\(Ha:\)碌\( > 10;\alpha = .01;n = 24\)\(\)
c.\(Ha:\)碌\( > 10;\alpha = .10;n = 9\)
d.\(Ha:\)碌 <\(10:\alpha = .01;n = 12\)
e.\(Ha:\)碌\( \ne 10;\alpha = .10;n = 20\)
f. \(Ha:\)碌<\(10;\alpha = .05;n = 4\)
Accuracy of price scanners at Walmart. Refer to Exercise 6.129 (p. 377) and the study of the accuracy of checkout scanners at Walmart stores in California. Recall that the National Institute for Standards and Technology (NIST) mandates that for every 100 items scanned through the electronic checkout scanner at a retail store, no more than two should have an inaccurate price. A study of random items purchased at California Walmart stores found that 8.3% had the wrong price (Tampa Tribune, Nov. 22, 2005). Assume that the study included 1,000 randomly selected items.
a. Identify the population parameter of interest in the study.
b. Set up H0 and Ha for a test to determine if the true proportion of items scanned at California Walmart stores exceeds the 2% NIST standard.
c. Find the test statistic and rejection region (at ) for the test.
d. Give a practical interpretation of the test.
e. What conditions are required for the inference, part d, to be valid? Are these conditions met?
Specify the differences between a large-sample and a small-sample test of a hypothesis about a population mean m. Focus on the assumptions and test statistics.
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