Exam 8: Regression, Associations, and Predictive Modeling

Does regular exercise decrease the risk of cancer? A researcher finds 200 women over 50 who Exercise regularly, pairs each with a woman who has a similar medical history but does not Exercise, then follows subjects for 10 years to see which group develops more cancer. This is a

What is the probability that a student from this class eats breakfast but does not floss?

Should the admissions officers conclude that the percentage of private school students in their applicant pool is lower than the statewide enrollment rate of 12%? Explain.

Decorate A store sells ornaments for Christmas trees. The prices of the ornaments are roughly normally distributed with a mean of $7.65 and a standard deviation of $1.45. a. What is the probability that a randomly selected ornament will cost more than $10? b. If eight ornaments are randomly selected, what is the probability that exactly 3 of them cost over $10?

The principal of a small elementary school wants to select a simple random sample of 24 students. The school has 12 classrooms with 18 students in each class. She decides to randomly select two Students from each classroom. Is this a simple random sample?

The service contract for the printer estimates a mean annual cost of $120 with standard deviation of $30. What is the expected value and standard deviation of the total cost for the service contracts on computer and printer?

Describe the W's, if the information is given: • Who: • What: • When: • Where: • How: • Why:

Still strange dice • The six faces of Die A show a 1 and five 3's. • Die B has four 2's and two 6's. Suppose you use these two dice in a competition against another player. You will roll one of the dice and your opponent will roll the other one. The winner is the person who rolls the higher number. You get first choice of dice and want to win. Would you pick Die A or Die B? Explain why.

A company checking the productivity of its assembly line monitored a random sample of workers For several days. They found that a 95% confidence interval for the mean number of items Produced daily by each worker was (23,27). Which is true?

The standard deviation of the data displayed in this dotplot is most likely to be …

Test an appropriate hypothesis and state your conclusion.

Interpret the confidence interval in this context.

What is the probability that two customers in a row get only 10% discounts?

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.

Sleep Do more than 50% of U.S. adults feel they get enough sleep? According to Gallup's December 2004 Lifestyle poll, 55% of U.S. adults said that that they get enough sleep. The poll was based on a random sample of 1003 U.S. adults. Test an appropriate hypothesis and state your conclusion in the context of the problem.

Find the value of the correlation coefficient and interpret this value in context.

A wildlife biologist wants to determine the mean weight of adult red squirrels. She captures 10 Squirrels she believes to be representative of the species and weighs them, finding a mean of 12.32 Grams and standard deviation of 1.88gm. Assuming these squirrels can be considered a random Sample of all red squirrels which of the following formulas gives a 95% confidence interval for the Mean weight of all squirrels?

Which statement about re-expressing data is not true? I. Unimodal distributions that are skewed to the left will be made more symmetric by taking the Square root of the variable. II. A curve in which the direction of the association changes from negative to positive Will not benefit from re-expression. III. One goal of re-expression may be to make the variability of the response variable more Uniform.

What is the probability that exactly 2 of the first 10 customers buy magazines? Show work.

Cigarette taxes New York public health officials report that currently 22% of adults smoke (Ithaca Journal, 1/12/04). They hope that newly increased state cigarette taxes will reduce this rate. They plan to check in December by selecting a random sample of 1200 New Yorkers to estimate again the percentage of adults who smoke. a. Verify that a Normal model is a useful approximation for the binomial in this situation. b. In that December sample, how many smokers would it take to convince you that the percentage of NY adults who smoke had decreased significantly? Explain.