Inference for Distributions of Categorical Data

 Assuming $H_0$ is true, the expected number of Hispanic drivers who would receive a ticket is

(a) 8

(c) 11.

(e) 12.

(b) 10.36

(d) 11.84

T11.5. We compute the value of the${\chi }^2$statistic to be $6.58$. Assuming that the conditions for inference are met, the P-value of our test is

(a) greater than $0.20$

(b) between $0.10$ and $0.20$.

(c) between $0.05$ and $0.10$.

(d) between$0.01$ and $0.05$

(e) less than $0.01$

The category that contributes the largest component to the${\chi }^2$statistic is

(a) White.

(c) Hispanic.

(b) Black.

(d) Other.

(e) The answer cannot be determined since this is only a sample.

The appropriate degrees of freedom for the $x^2$ statistic is

(a) 1 .

(b) 2 .

(c) 3 .

(d) 4 .

(e) 5 .

The expected count of cases of lymphoma in homes with an HCC is

(a) $\frac{79·31}{215}$.

(b) $\frac{10·21}{215}$.

(c) $\frac{79·31}{10}$.

(d) $\frac{136·31}{215}$.

(e) None of these.

 Which of the following may we conclude, based on the test results?

(a) There is strong evidence of an association between wiring configuration and the chance that a child will develop some form of cancer.

(b) HCC either cause 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 much evidence of an association between wiring configuration and the type of cancer that caused the deaths of children in the study.

A Type I error would occur if we conclude that

(a) HCC wiring caused cancer when it actually didn't.

(b) HCC wiring didn't cause cancer when it actually did.

(c) there is no association between the type of wiring and the form of cancer when there actually is an association.

(d) there is an association between the type of wiring and the form of cancer when there actually is no association.

(e) the type of wiring and the form of cancer have a positive correlation when they actually don't.

A large distributor of gasoline claims that $60\%$all cars stopping at their service stations choose regular unleaded gas and that premium and supreme are each selected $20\%$of the time. To investigate this claim, researchers collected data from a random sample of drivers who put gas in their vehicles at the distributor's service stations in a large city. The results were as follows:

Carry out a significance test of the distributor's claim. Use a $5\%$significance level.

A study conducted in Charlotte, North Carolina, tested the effectiveness of three police responses to spouse abuse: (1) advise and possibly separate the couple, (2) issue a citation to the offender, and (3) 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 650 cases in the study. Each case was classified according to whether the abuser was subsequently arrested within six months of the original incident.

(a) Explain the purpose of the random assignment in the design of this study.

(b) Construct a well-labeled graph that is suitable for comparing the effectiveness of the three treatments.

(c) We want to use these data to perform a test of $H_0:$$p_1=p_2=p_3$ where $p_i=$

the true proportion of spouse abusers like the ones in this study who would be arrested again within six months after receiving treatment \(i\). State an appropriate alternative hypothesis.

(d) Assume that all the conditions for performing the test in part (b) are met. The test yields  ${\chi }^2=5.063$ and a P-value of $0.0796$ Interpret this P-value in context. What conclusion should we draw from the study?

 In the United States, there is a strong relationship between education and smoking: well-educated people are less likely to smoke. Does a similar relationship hold in France? To find out, researchers recorded the level of education and smoking status of a random sample of 459 French men aged 20 to 60 years. 11 The two-way table below displays the data.

(a) Is the relationship between smoking status and educational level statistically significant? Give appropriate evidence to support your answer.

(b) Which cell in the table contributes most to the relationship in part (a)? Justify your answer.