Exam 8: Regression, Associations, and Predictive Modeling

Suppose a Normal model describes the number of pages printer ink cartridges last. If we keep track Of printed pages for the 47 printers at a company's office, which must be true? I. The page counts for those ink cartridges will be normally distributed. II. The histogram for those page counts will be symmetric. III. 95% of those page counts will be within 2 standard deviations of the mean.

Explain what your P-value means in this context.

At one SAT test site students taking the test for a second time volunteered to inhale supplemental Oxygen for 10 minutes before the test. In fact, some received oxygen, but others (randomly Assigned) were given just normal air. Test results showed that 42 of 66 students who breathed Oxygen improved their SAT scores, compared to only 35 of 63 students who did not get the oxygen. Which procedure should we use to see if there is evidence that breathing extra oxygen can help Test-takers think more clearly?

In an experiment the primary purpose of blinding is to reduce …

Bowling A large corporation sponsors bowling leagues for its employees. The mean score for men was 154 pins with a standard deviation of 9 pins, while the women had mean score 144 pins and standard deviation 12 pins. At the end of the season the league holds a tournament that randomly pairs men and women as opponents in the first round. a. On average, how much do you expect the man to win by? b. Estimate the standard deviation of the differences in the competitor's scores. c. What assumption did you make in determining the standard deviation?

Copy machines A manufacturer claims that lifespans for their copy machines (in months) can be described by a Normal model N(42,7). Show your work. a. Draw and clearly label the model. b. A company with a several large office buildings buys 200 of these copiers. The salesman tells the boss "190 (95%) of your new copiers will last between _____ and _____ months." Comment on this claim. c. What is the 3rd quartile of copier lifespans? d. What percent of the copiers are expected to fail before 36 months? e. The manufacturer wants to reduce the 36-month failure rate to only 10%. Assuming the mean lifespan will stay the same, what standard deviation must they achieve? f. Briefly explain what that change in standard deviation means in this context. g. A competing manufacturer says that not only will 90% of their copiers last at least 36 months, 65% will last at least 42 months. What Normal model parameters is that manufacturer claiming? Show your work.

Suppose that a Normal model describes fuel economy (miles per gallon) for automobiles and that a Saturn has a standardized score (z-score) of +2.2. This means that Saturns . . .

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

Candy packaging Marketing researchers wonder if the color and type of a candy's packaging may influence sales of the candy. They manufacture test packages for chocolate mints in three colors (white, green, and silver) and three types (box, bag, and roll). Suspecting that sales may depend on a combination of package color and type, the researchers prepare nine different packages, then market them for several weeks in convenience stores in various locations. In this experiment. a. what are the experimental units? b. how many factors are there? c. how many treatments are there? d. what is the response variable?

Interpret the slope of your model in context.

Explain what 90% confidence means in this context.

In regression an observation has high leverage when

Which statement correctly compares t-distributions to the Normal distribution? I. t distributions are also mound shaped and symmetric. II. t distributions are more spread out than the normal distribution. III. As degrees of freedom increase, the variance of t distributions becomes larger.

Create a model to predict postal rates from the year.

We have calculated a confidence interval based upon a sample of n = 200. Now we want to get a Better estimate with a margin of error only one fifth as large. We need a new sample with …

Studying for exams A philosophy professor has found a correlation of 0.80 between the number of hours students study for his exams and their exam performance. During the time he collected the data, students studied an average of 10 hours with a standard deviation of 2.5 hours, and scored an average of 80 points with a standard deviation of 7.5 points. a. Create a linear model to estimate the number of points a student will score on the next exam from the number of hours the student studies. b. If a student studies for 15 hours, what score should the student expect on the next exam? Show your work.

It is generally believed that nearsightedness affects about 12% of children. A school district gives vision tests to 133 incoming kindergarten children. a. Describe the sampling distribution model 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 15% of the children will be found to be nearsighted?

Depression A recent psychiatric study from the University of Southampton observed a higher incidence of depression among women whose birth weight was less than 6.6 pounds than in women whose birth weight was over 6.6 pounds. Based on a P-value of 0.0248 the researchers concluded there was evidence that low birth weights may be a risk factor for susceptibility to depression. Explain in context what the reported P-value means.

A poll of 120 Ithacans found that 30 had visited the Museum of the Earth, and that 80 had been to Home Depot. If it appeared that going to Home Depot and going to the Museum of the Earth were Independent events, how many of those polled had been to both?

More dogs are being diagnosed with thyroid problems than have been diagnosed in the past. A Researcher identified 50 puppies without thyroid problems and kept records of their diets for Several years to see if any developed thyroid problems. This is a(n)