Exam 8: Regression, Associations, and Predictive Modeling

Find the expected number of repairs this kind of computer is expected to need each year. Show your work.

How do sports salaries compare? Two sets of histograms below show the distributions of salaries for Major League Baseball and the National Football League. Give two reasons why the second set of histograms makes it easier to compare the distributions. Then write a few sentences comparing the salary distributions for the two sports.

Create and interpret a 90% confidence interval.

If we want to discuss any gaps and clusters in a data set, which of the following should not be Chosen to display the data set?

Owners of a minor league baseball team believe that a Normal model is useful in projecting the number of fans who will attend home games. They use a mean of 8500 fans and a standard deviation of 1500 fans. Draw and clearly label this model.

Describe the kind of bias that might be present if the administration decides that instead of subjecting people to random testing they'll just… a. drop grains of rice on the aerial photo of the hill and inspect the trees that had rice land on them. b. ask the farmer to choose which trees he would like tested.

Find and interpret a 95% confidence interval for the slope of the regression equation.

Write the advocates' null and alternative hypotheses.

Music and grades (True Story) A couple of years ago, a local newspaper published research results claiming a positive association between the number of years high school children had taken instrumental music lessons and their performances in school (GPA). a. What does "positive association" mean in this context? b. A group of parents then went to the School Board demanding more funding for music programs as a way to improve student chances for academic success in high school. As a statistician, do you agree or disagree with their reasoning? Explain briefly.

The monkeys manage to go a whole week without someone bumping their head. One of the kangaroos insists that they are due for an injury. Another says they must be getting better at their jumping skills. Do you think they're due for a crash?

Another company's sales increase by the same percent each year. This growth is . . .

Basketball player heights Assume the heights of high school basketball players are normally distributed. For boys the mean is 74 inches with a standard deviation of 4.5 inches, while girl players have a mean height of 70 inches and standard deviation 3 inches. At a mixed 2-on-2 tournament teams are formed by randomly pairing boys with girls as teammates. a. On average, how much taller do you expect the boy to be? b. What will be the standard deviation of the difference in teammates' heights? c. On what fraction of the teams would you expect the girl to be taller than the boy?

A consultant talked the group into gathering a larger sample. Will the power of the test increase, decrease, or remain the same?

Which statement about correlation is true? I. Regression based on data that are summary statistics tends to result in a higher correlation. II. If $\text { If } r ^ { 2 } = 0.95$ 0)95, the response variable increases as the explanatory variable increases. III. An outlier always decreases the correlation.

State your conclusion.

Book sales A publishing company pays its sales staff $600 a week plus a commission of $0.50 per book sold. For example, a salesman who sold 440 books earned 600 + 0.50(440) = $820. a. The table shows summary statistics for the number of books the large sales staff sold last week. Fill in the table to show the statistics for the pay these people earned. Statistic Books Sold \ Earned Mean 640 St. dev. 360 IQR 450 Maximum 1420 b. The newest employee had a pretty good week. Among all the salespeople her pay corresponded to a z-score of +1.80. What was the z-score of the number of books she sold?

A consumer group collected information on HDTVs . They created a linear model to estimate the Cost of an HDTV (in $) based on the screen size (in inches). Which is the most likely value of the Slope of the line of best fit?

There are 1,237 trees on the hill. Explain how to use a random digit table to select a simple random sample of 20 trees. Then use the random digit table below to select the first five trees for your sample.

Which of the following is not a goal of re-expressing data?

To plan the course offerings for the next year a university department dean needs to estimate what Impact the "No Child Left Behind" legislation might have on the teacher credentialing program. Historically, 40% of this university's pre-service teachers have qualified for paid internship Positions each year. The Dean of Education looks at a random sample of internship applications to See what proportion indicate the applicant has achieved the content-mastery that is required for The internship. Based on these data he creates a 90% confidence interval of (33%, 41%). Could this Confidence interval be Used to test the hypothesis H0: p = 0.40 versus HA: p < 0.40 at the α = 0.05 level of significance?