Exam 8: Regression, Associations, and Predictive Modeling

Time Wasted A group of students decide to see if there is link between wasting time on the internet and GPA. They don't expect to find an extremely strong association, but they're hoping for at least a weak relationship. Here are the findings. linear regression results: Dependent Variable: GPA Sample size: 10 R (correlation coefficient) =-0.37199274 R-sq =0.1383786 s=0.85365134 Parameter Estimate Std. Err. Intercept 4.06191 0.74405 Hours/week -0.0297 0.02616 a. How strong is the relationship the students found? Describe in context with statistical justification. One student is concerned that the relationship is so weak, there may not actually be any relationship at all. To test this concern, he runs a simulation where the 10 GPA's are randomly matched with the 10 hours/week. After each random assignment, the correlation is calculated. This process is repeated 100 times. Here is a histogram of the 100 correlations. The correlation coefficient of -0.371 is indicated with a vertical line. b. Do the results of this simulation confirm the suspicion that there may not be any relationship? Refer specifically to the graph in your explanation.

Too much TV? A father is concerned that his teenage son is watching too much television each day, since his son watches an average of 2 hours per day. His son says that his TV habits are no different than those of his friends. Since this father has taken a stats class, he knows that he can actually test to see whether or not his son is watching more TV than his peers. The father collects a random sample of television watching times from boys at his son's high school and gets the following data: 1.9 2.3 2.2 1.9 1.6 2.6 1.4 2.0 2.0 2.2 Is the father right? That is, is there evidence that other boys average less than 2 hours of television per day? Conduct a hypothesis test, making sure to state your conclusions in the context of the problem.

Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than $97 \%$ good parts $\left( \mathrm { H } _ { 0 } : p = 0.97 \right.$ and $\left. \mathrm { H } _ { \mathrm { A } } : p > 0.97 \right)$ . The test results in a $P$ -value of $0.122$ . Unknown to the manufacturer, the machine is actually producing $99 \%$ good parts. What probably happens as a result of the testing?

Internet access A recent Gallup poll found that 28% of U.S. teens aged 13-17 have a computer with Internet access in their rooms. The poll was based on a random sample of 1028 teens and reported a margin of error of $\pm 3 \%$ 3%. What level of confidence did Gallup use for this poll?

Do you think a linear model is appropriate here? Explain.

Listed below are the names of the 20 pharmacists on the hospital staff. Use the random numbers listed below to select three of them to be in the sample. Clearly explain your method. Pastore Back Spiridinov Ahl Hedge MacDowell Schissel Novelli Lavine Kaplan Highland Roundy Grubb Markowitz Glass Davies Golkowski Reeves Janis Yen

Which is true about randomized experiments? I. Randomization reduces the effects of confounding variables. II. Random assignment of treatments allows results to be generalized to the larger population. III. Blocking can be used to reduce the within-treatment variability.

You could win a $1000 prize by tossing a coin in one of two games. To win Game A, you must get Exactly 50% heads. To win Game B, you must get between 45% and 55% heads. Although which Game you must play will be chosen randomly, then you may decide whether to toss the coin 20 Times or 50 times. How many tosses would you choose to make?

Interpret s in context.

A researcher investigating whether joggers are less likely to get colds than people who do not jog Found a P-value of 3%. This means that:

Interpret the intercept of your model in context.

The United States Census collects data on many variables about individuals and households. Which variable is categorical?

Preservative Leather furniture used in public places can fade, crack, and deteriorate rapidly. An airport manager wants to see if a leather preservative spray can make the furniture look good longer. He buys eight new leather chairs and places them in the waiting area, four near the south-facing windows and the other four set back from the windows as shown. He assigned the chairs randomly to these spots. a. Use the random numbers given to decide which chairs to spray. Explain your method clearly. b. Briefly explain why your assignment strategy is important in helping the manager assess the effectiveness of the leather preservative.

Blood pressure and cholesterol Suppose that both blood pressure and cholesterol levels of adult women can be described with Normal models, and that the correlation between these variables is 0.60. If a woman's blood pressure places her at the 88th percentile, at what percentile would you predict her cholesterol level to be?

Show three trials by clearly labeling the random number table given below. Specify the outcome for each trial.

The next day, a young girl reveals that her older brother also went trick-or-treating, but didn't want to admit that he participated. He was added to the data set and these are the results. Dependent Variable: candy Sample size: 10 $R$ (correlation coefficient $) = 0.76362369$ $\mathrm { R } - \mathrm { sq } = 0.58312115$ $s = 12.709041$ Parameter Estimate Std. Err. Intercept 13.569231 9.0783516 Age 3.4038462 1.0175376 Describe the effect of this new candy collector on the regression model.

A statistics professor wants to see if more than 80% of her students enjoyed taking her class. At the End of the term, she takes a random sample of students from her large class and asks, in an Anonymous survey, if the students enjoyed taking her class. Which set of hypotheses should she Test?

Doctors at a technology research facility randomly assigned equal numbers of people to use computer keyboards in two rooms. In one room a group of people typed a manuscript using standard keyboards, while in the other room people typed the same manuscript using ergonomic keyboards to see if those people could type more words per minute. After collecting data for several days the researchers tested the hypothesis $\mathrm { H } _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ against the one-tail alternative and found $P = 0.22$ . Which is true?

If we wish to compare the average PSAT scores of boys and girls taking AP* Statistics at a high School, which would be the best way to gather these data?

Identify the following: a. the subjects b. the factor(s) and the number of level(s) for each c. the number of treatments d. whether or not the experiment is blind (or double-blind) e. the response variable