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Chapter 7: Q112S (page 442)
If the rejection of the null hypothesis of a particular test would cause your firm to go out of business, would you want to be small or large? Explain
The firm would want to be small.
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A random sample of 41 observations from a normal population possessed a mean \(\bar x = 88\) and a standard deviation s = 6.9.
a. Test \({H_0}:{\sigma ^2} = 30\) against \({H_a}:{\sigma ^2} > 30\). Use\(\alpha = 0.05.\)
Radon exposure in Egyptian tombs. Refer to the Radiation Protection Dosimetry (December 2010) study of radon exposure in Egyptian tombs, Exercise 6.30 (p. 349). The radon levels鈥攎easured in becquerels per cubic meter (\({{Bq} \mathord{\left/ {\vphantom {{Bq} {{m^3}}}} \right. \\} {{m^3}}}\) )鈥攊n the inner chambers of a sample of 12 tombs are listed in the table shown below. For the safety of the guards and visitors, the Egypt Tourism Authority (ETA) will temporarily close the tombs if the true mean level of radon exposure in the tombs rises to 6,000\({{Bq} \mathord{\left/ {\vphantom {{Bq} {{m^3}}}} \right. \\} {{m^3}}}\) . Consequently, the ETA wants to conduct a test to determine if the true mean level of radon exposure in the tombs is less than 6,000\({{Bq} \mathord{\left/ {\vphantom {{Bq} {{m^3}}}} \right. \\} {{m^3}}}\) , using a Type I error probability of .10. An SPSS analysis of the data is shown at the bottom of the page. Specify all the elements of the test: \({H_0}\,,{H_a}\) test statistic, p-value,\(\alpha \) , and your conclusion.
50 910 180 580 7800 4000 390 12100 3400 1300 11900 110
Intrusion detection systems. The Journal of Research of the National Institute of Standards and Technology (November鈥� December 2003) published a study of a computer intrusion detection system (IDS). The IDS is designed to provide an alarm whenever unauthorized access (e.g., an intrusion) to a computer system occurs. The probability of the system giving a false alarm (i.e., providing a warning when no intrusion occurs) is defined by the symbol , while the probability of a missed detection (i.e., no warning given when an intrusion occurs) is defined by the symbol . These symbols are used to represent Type I and Type II error rates, respectively, in a hypothesis-testing scenario
a. What is the null hypothesis, ?
b. What is the alternative hypothesis,?
c. According to actual data collected by the Massachusetts Institute of Technology Lincoln Laboratory, only 1 in 1,000 computer sessions with no intrusions resulted in a false alarm. For the same system, the laboratory found that only 500 of 1,000 intrusions were actually detected. Use this information to estimate the values of and .
Calories in school lunches. A University of Florida economist conducted a study of Virginia elementary school lunch menus. During the state-mandated testing period, school lunches averaged 863 calories (National Bureau of Economic Research, November 2002). The economist claims that after the testing period ends, the average caloric content of Virginia school lunches drops significantly. Set up the null and alternative hypotheses to test the economist鈥檚 claim.
Companies that produce candies typically offer different colors of their candies to provide consumers a choice. Presumably, the consumer will choose one color over another because of taste. Chance (Winter 2010) presented an experiment designed to test this taste theory. Students were blindfolded and then given a red or yellow Gummi Bear to chew. (Half the students were randomly assigned to receive the red Gummi Bear and half to receive the yellow Bear. The students could not see what color Gummi Bear they were given.) After chewing, the students were asked to guess the color of the candy based on the flavor. Of the 121 students who participated in the study, 97 correctly identified the color of the Gummi Bear.
a. If there is no relationship between color and Gummi Bear flavor, what proportion of the population of students would correctly identify the color?
b. Specify the null and alternative hypotheses for testing whether color and flavor are related.
c. Carry out the test and give the appropriate conclusion at Use the p-value of the test, shown on the accompanying SPSS printout, to make your decision.
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