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Chapter 11: Q 4. (page 716)
More P-values For each of the following, find the P-value using Table C. Then calculate a more precise value using technology.
a.
b.
Part (a) value
Part (b) value
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All current-carrying wires produce electromagnetic (EM) radiation, including the electrical wiring running into, through, and out of our homes. High-frequency EM radiation is thought to be a cause of cancer. The lower frequencies associated with household current are generally assumed to be harmless. To investigate the relationship between current configuration and type of cancer, researchers visited the addresses of a random sample of children who had died of some form of cancer (leukemia, lymphoma, or some other type) and classified the wiring configuration outside the dwelling as either a high-current configuration (HCC) or a low-current configuration (LCC). Here are the data:
Computer software was used to analyze the data. The output included the value
Which of the following may we conclude, based on the chi-square test results?
a. There is convincing evidence of an association between wiring configuration and the chance that a child will develop some form of cancer.
b. HCC either causes cancer directly or is a major contributing factor to the development of cancer in children.
c. Leukemia is the most common type of cancer among children.
d. There is not convincing evidence of an association between wiring configuration and the type of cancer that caused the deaths of children.
e. There is convincing evidence that HCC does not cause cancer in children.
A study conducted in Charlotte, North Carolina, tested the effectiveness of three police responses to spouse abuse: advise and possibly separate the couple, issue a citation to the offender, and arrest the offender. Police officers were trained to recognize eligible cases. When presented with an eligible case, a police officer called the dispatcher, who would randomly assign one of the three available treatments to be administered. There were a total of cases in the study. Each case was classified according to whether the abuser was arrested within months of the original incident.
a. Explain the purpose of the random assignment in the design of this study.
b. State an appropriate pair of hypotheses for performing a chi-square test in this setting.
c. Assume that all the conditions for performing the test in part (b) are met. The test yields and a. Interpret this P-value.
d. What conclusion should we draw from the study?
Distance from home A study of first-year college students asked separate random samples of students from private and public universities the following question: 鈥淗ow many miles is this university from your permanent home?鈥� Students had to choose from the following options:or fewer, to to to to , or more than . Here is the two-way table summarizing the responses:
a. Should we use a chi-square test for homogeneity or a chi-square test for independence in this setting? Justify your answer.
b. State appropriate hypotheses for performing the type of test you chose in part (a). Here is Minitab output from a chi-square test.
c. Check that the conditions for carrying out the test are met.
d. Interpret the P-value. What conclusion would you draw?
Do students who read more books for pleasure tend to earn higher grades in English? The boxplots show data from a simple random sample of 79 students at a large high school. Students were classified as light readers if they read fewer than 3 books for pleasure per year. Otherwise, they were classified as heavy readers. Each student鈥檚 average English grade for the previous two
marking periods was converted to a GPA scale, where A=4.0, A鈭�=3.7, B+=3.3
Reading and grades (3.2) The scatterplot shows the number of books read and the English grade for all 79 students in the study. The least-squares regression line y^=3.42+0.024x has been added to the graph.
a. Interpret the slope and y intercept.
b. The student who reported reading 17 books for pleasure had an English GPA of 2.85. Calculate and interpret this student鈥檚 residual.
c. For this linear model, r2=0.083 Interpret this value.
Skittles庐 Statistics teacher Jason Mole sky contacted Mars, Inc., to ask about the color distribution for Skittles candies. Here is an excerpt from the response he received: 鈥淭he original flavor blend for the Skittles Bite Size Candies is lemon, green apple, orange, strawberry and grape. They were chosen as a result of consumer preference tests we conducted. The flavor blend is percent of each flavor.鈥�
a. State appropriate hypotheses for a significance test of the company鈥檚 claim.
b. Find the expected counts for a random sample of candies.
c. How large a test statistic would you need to have significant evidence against the company鈥檚 claim at the 伪=0.05 level? At the level?
d. Create a set of observed counts for a random sample of candies that gives a value between and Show the calculation of your chi-square test statistic.
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