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Exam 8: Regression, Associations, and Predictive Modeling

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Question 201

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A survey of local car dealers revealed that 64% of all cars sold last month had CD players, 28% had alarm systems, and 22% had both CD players and alarm systems. a. What is the probability one of these cars selected at random had neither a CD player nor an alarm system? b. What is the probability that a car had a CD player unprotected by an alarm system? c. What is the probability a car with an alarm system had a CD player? d. Are having a CD player and an alarm system disjoint events? Explain.

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a. or and , so (neither
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Question 202

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What is the probability that there is at least one customer to win a 50% discount among the first five customers that enter the store?

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For a more definitive evaluation of reading level the editor wants to estimate the text's mean word length to within 0.5 letters with 98% confidence. How many randomly selected words does she need to use?

Passing the test Assume that 70% of teenagers who go to take the written drivers license test have studied for the test. Of those who study for the test, 95% pass; of those who do not study for the test, 60% pass. What is the probability that a teenager who passes the written drivers license test did not study for the test?

The blood drive has a total of 150 donors. Assuming this is a typical number of donors for a school blood drive, what would be the mean and standard deviation of the number of donors who have Type B blood?

1. It is generally believed that electrical problems affect about 14% of new cars. An automobile mechanic conducts diagnostic tests on 128 new cars on the lot. a. Describe the sampling distribution for the sample proportion by naming the model and telling its mean and standard deviation. Justify your answer. b. Sketch and clearly label the model. c. What is the probability that in this group over 18% of the new cars will be found to have electrical problems?

Comment on any unusual data point or points in the data set. Explain.

Create and interpret a 95% confidence interval for the slope of the regression line.

Graduation tests Many states mandate tests that have to be passed in order for students to graduate with a high school diploma. A local school superintendent believes that after-school tutoring will improve the scores of students in his district on the state's graduation test. A tutor agrees to work with 15 students for a month before the superintendent will approach the school board about implementing an after-school tutoring program. The after-school tutoring program will be implemented if student scores increase by more than 20 points. The superintendent will test a hypothesis using α = 0.02 . a. Write appropriate hypotheses (in words and in symbols). b. In this context, which do you consider to be more serious - a Type I or a Type II error? Explain. c. After this trial produced inconclusive results, the superintendent decided to test the after-school tutoring program again with another group of students. Describe two changes he could make in the trial to increase the power of the test, and explain the disadvantages of each.

Management decided to extend the incentive program so that the decision can be made on three months of data instead. Will the power increase, decrease, or remain the same?

Gas mileage Hoping to improve the gas mileage of their cars, a car company has made an adjustment in the manufacturing process. Random samples of automobiles coming off the assembly line have been measured each week that the plant has been in operation. The data from before and after the manufacturing adjustments were made are in the table. It is believed that measurements of gas mileage are normally distributed. Write a complete conclusion about the manufacturing adjustments based on the statistical software printout shown below.

A researcher notes that there is a positive correlation between the temperature on a summer day and the number of bees that he can count in his garden over a 5-minute time span. a. Describe what the researcher means by a positive correlation. b. If the researcher calculates the correlation coefficient using degrees Fahrenheit instead of Celsius, will the value be different?

Was your test one-tail upper tail, lower tail, or two-tail? Explain why you chose that kind of test in this situation.

Which of the following is not a source of caution in regression between two variables?

As part of a survey, students in a large statistics class were asked whether or not they ate breakfast that morning. The data appears in the following table: Is there evidence that eating breakfast is independent of the student's sex? Test an appropriate hypothesis. Give statistical evidence to support your conclusion.

Explain what 95% confidence means in this context.

Commuting to work The table shows how a company's employees commute to work. a. What is the marginal distribution (in %) of mode of transportation (Car, Bus, Train)? b. What is the conditional distribution (in %) of mode of transportation (Car, Bus, Train) for management? c. What kind of display would you use to show the association between job class and mode of transportation? (Just name a graph.) d. Do job classification and mode of transportation appear to be independent? Give statistical evidence to support your conclusion.

Gun control Two friends who strongly disagree on whether there should be stricter regulation of guns in this country want to conduct a poll of the students in their school to see which side most students agree with. Each came back with a different version of the question they want to ask. Version 1: Do you think the government should respect our 2nd Amendment rights and allow lawabiding citizens to own guns? Version 2: In the wake of recent mass shootings, should laws be passed to keep guns out of the hands of people with a history of violence? a. Which version would make it seem like people oppose stricter gun regulation? What kind of bias is this? b. Is the version you did not pick in part a less biased? c. Is it reasonable for a person to respond 'yes' to both questions?

The January 2005 Gallup Youth Survey telephoned a random sample of 1,028 U.S. teens and asked These teens to name their favorite movie from 2004. Napoleon Dynamite had the highest percentage With 8% of teens ranking it as their favorite movie. Which is true? I. The population of interest is all U.S. teens. II. 8% is a statistic and not the actual percentage of all U.S. teens who would rank this movie as Their favorite. III. This sampling design should provide a reasonably accurate estimate of the actual percentage of All U.S. teens who would rank this movie as their favorite.

Absorption rates into the body are important considerations when manufacturing a generic version Of a brand-name drug. A pharmacist read that the absorption rate into the body of a new generic Drug (G) is the same as its brand-name counterpart (B) . She has a researcher friend of hers run a Small experiment to test H0: µG - µB = 0 against the alternative HA: µG - µB ≠ 0) Which of the Following would be a Type I error?